arXiv subjects

M. Lakshmanan

Publications and source records attributed to M. Lakshmanan.

At least 19 recordsLinked to original sources

arXiv2026

Nondegenerate bright solitons and their interactions in the generalized coupled nonlinear Schroedinger system

It is known that the generalized coupled nonlinear Schroedinger (GCNLS) equations can be reduced to the basic vector nonlinear Schroedinger models through various symmetry reductions. By using such reductions, soliton solutions of several interesting types can be obtained for the GCNLS system. In this paper, we show how the non-degenerate soliton solutions can be derived using one such reduction and analyze the various special features associated with the resulting soliton solutions. We find that the obtained non-degenerate soliton solutions exhibit breathing behavior, characterized by a breathing frequency. We also show that the vector solitons emerging from the reduction undergo elastic collisions with the standard phase shift, similar to the non-degenerate solitons of other coupled nonlinear Schroedinger models. Further, they undergo interesting energysharing collisions when they interact with the already known bright solitons. These collision scenarios are further confirmed by an appropriate asymptotic analysis. We have also analyzed the stability of the obtained vector solitons and found that they are stable against random perturbations. The results presented here enhance the understanding of the nature and dynamics of non-degenerate vector solitons.

nlin.PS↗

arXiv2026

Collective dynamics in a one-dimensional Heisenberg ferromagnetic spin chain

We investigate the different oscillatory modes, namely, complete synchronization, inphase synchronization, antiphase synchronization and desynchronization in a one-dimensional anisotropic Heisenberg ferromagnetic spin chain consisting of a large number of spins. By solving the associated Landau-Lifshitz-Gilbert-Slonczewski equation for the spins we show the simultaneous existence of the above mentioned oscillatory modes in the spins. We observe that when the number of the spins is large the synchronization is lost between the spins; however, we identify that the field-like torque is able to induce synchronous oscillations of the spins in the chain again. We also confirm the agreement of the numerically obtained values of the frequency of the inphase synchronized oscillations with the analytically obtained values.

nlin.PS↗

arXiv2026

Integrable motion of curves associated with the Fokas-Lenells equation and related spin system

In this article, we study the gauge equivalence between the integrable Fokas- Lenells equation (FLE) and an associated spin equation through a gauge transformation and the zero curvature condition. We also construct the Lax pair for the generalized spin equation to confirm its integrability. Further, by mapping a generalized spin system on a moving space curve in R3, we show its geometrical equivalence with the FLE. In particular, the associated evolution equations for the curvature and torsion of the space curve are shown to be equivalent to the FLE through a complicated complex transformation unlike the case of the well known Heisenberg spin equation and the nonlinear Schr\"odinger equation.

nlin.SI↗

arXiv2026

Bright soliton interactions in the variable coefficient Fokas-Lenells equation, Conservation laws, Modulation instability and Soliton tunneling

We present here a study of the bright soliton dynamics in an inhomogeneous fibre by means of variable coefficient Fokas-Lenells equation with time varying dispersion, nonlinearity and gain/loss parameter. At first, we propose our system that governs the propagation of ultrashort pulses in an inhomogeneous fibre. Secondly, under a suitable gauge transformation, we transform the system into a simplified form of variable coefficient Fokas-Lenells equation. The Lax integrability and conservation laws are exhibited. We also study the stability of the generalised plane wave against small amplitude perturbations. Thereafter, by using a nonstandard Hirota bilinearization method with the help of a suitable auxiliary function, we obtain the bright one soliton, two soliton and provide a scheme for obtaining N-bright soliton solutions. The elastic collision dynamics of the two solitons is studied using asymptotic analysis. We also investigate the soliton acceleration/retardation under a suitable choice of dispersion and nonlinearity coefficients. Finally, the dramatic effect of the nonlinear tunnelling of the bright one and two-soliton is also studied under some Gaussian dispersion or nonlinearity.

nlin.PS↗

arXiv2026

Self-oscillations induced by self-induced torque in magnetic double tunnel junction

Self-oscillations of the magnetization due to self-induced torque (SIT) in a magnetic double tunnel junction that consists of perpendicularly polarized, pinned and free layers is investigated along with the field-like torque (FLT). The associated Landau-Lifshitz-Gilbert-Slonczewski equation is numerically analysed to exhibit the oscillations of magnetization driven by the current. From the numerical analysis, we show that the SIT is essential to generate oscillations in the order of GHz and without it the magnetization reaches steady state after exhibiting switching. Without FLT, the frequency of the oscillations decreases with the current while the power of oscillations increases. In the presence of the negative strength of the FLT the power spectral density confirms that the frequency, power and the Q-factor increase with the current. Also the tunability range and the rate at which the frequency enhances increase with the magnitude of the FLT.

cond-mat.mes-hall↗

arXiv2025

Linear coupling effect induced beating non-degenerate vector solitons

In this paper, we propose an alternative approach to generate a new class of beating vector solitons. Unlike earlier procedures that use dark-bright or bright-dark soliton solutions to generate beating solitons, the method described here utilizes non-degenerate vector soliton solutions of the Manakov system. It involves linear superposition of such soliton solutions along with an intensity switching mechanism facilitated by cross-coupling between the optical modes. We find that the obtained beating solitons collide elastically with themselves and keep their beating feature unchanged after the collision. We also find that their beating nature can be controlled by allowing them to collide with degenerate beating solitons exhibiting energy-sharing collisions. The results presented in this work will provide new insights into beating solitons in Bose-Einstein condensates, nonlinear optics, and related areas of research.

nlin.PS↗

arXiv2025

General two-component long-wave short-wave resonance interaction system: Non-degenerate vector solitons and their collision dynamics

In this paper, we demonstrate the emergence of non-degenerate bright solitons and summarize their several interesting features in a completely integrable two-component long-wave-short-wave resonance interaction model with a general form of nonlinearity coefficients. Through the classical Hirota's bilinear method, we obtain a fully non-degenerate $N$-soliton solution in Gram determinant form for this LSRI model. Depending on the choice of velocity conditions, the obtained non-degenerate fundamental soliton is classified into two types, namely ($1,1,1$)- and ($1,1,2$)-non-degenerate one solitons. We then show that the basic ($1,1,1$)-non-degenerate soliton exhibits novel profile structures, including a double-hump, a special flat-top, and a conventional single-hump profile, and ($1,1,2$)-non-degenerate soliton admits two-soliton like oblique collision, a behavior akin to KP line soliton interaction with a short stem structure. A detailed asymptotic analysis is carried out to study the long time behavior of ($1,1,1$)-non-degenerate solitons and it reveals that they undergo both shape-preserving and shape-changing collisions. However, our analysis confirms that the shape changing collision between these solitons become elastic in nature after appropriate shift of time coordinates. Further, we identified that the ($1,1,2$)-non-degenerate solitons also undergo elastic collision. In addition, we have also investigated the formation or suppression of breathing phenomena during collision between a degenerate soliton and a ($1,1,1$)-non-degenerate soliton. For completeness, we also point out the collision scenario between the completely degenerate solitons. The results presented in this paper are broadly applicable to Bose-Einstein condensates, nonlinear optics, plasma physics, and other closely related fields.

nlin.PS↗

arXiv2025

A Quantum Approach to the Continuum Heisenberg Spin-Chain Model: Position-Dependent Mass Formalism and Pre-canonical Quantization

Painlevé's singularity structure analysis, combined with stereographic mapping, has previously been applied to a one-dimensional Heisenberg spin-chain continuum model which identified a Hamiltonian density for the static version of the Landau-Lifshitz equation. In this work, we explore the equivalence of the Hamiltonian density to the nonlinear sigma model. It reveals its non-standard form and can be interpreted as a position-dependent mass Hamiltonian density. We then proceed with the quantization of this Hamiltonian density using the pre-canonical quantization procedure. The resulting Schrödinger-like equation was found to take the form of a confluent Heun equation. By employing the functional Bethe-Ansatz method, we explicitly obtain the ground state and first excited state of the system. This analysis provides a comprehensive quantum description of the system, capturing the probabilistic structure of the field and information about the possible energy states of the spin system.

quant-ph↗

arXiv2025

Vector soliton molecules and their collisions

In recent times, bound soliton states have often been referred to as soliton molecules in the nonlinear optics literature. The striking analogies between photonic bound states and matter molecular structures in chemistry and physics have intensified studies on optical soliton molecules in both conservative and dissipative systems. In this paper, we demonstrate the existence of vector soliton molecules and their related isomer structures in a conservative optical fiber system by considering the integrable Manakov equation. We show their existence by applying the velocity resonance condition and appropriate choice of temporal separations to the degenerate $N=(\bar{N}+\bar{M})$-soliton solution. Then, we classify the obtained molecular states as either dissociated or synthesized molecular states based on the temporal locations of the constituent solitons. Furthermore, we analyze the collision properties of vector soliton molecules in the present conservative system. The collision scenarios reveal that the soliton molecules undergo intriguing energy-sharing collisions through energy redistribution among the modes. To characterize these collisions, we have carried out an appropriate asymptotic analysis and found that elastic collisions arise as a special case of energy-sharing collisions under specific choices of polarization constants. Finally, we numerically verify the robustness of vector soliton molecules. We believe that the results presented in this paper show potential for soliton molecule-based applications such as optical computation and multi-level encoding for communications.

nlin.PS↗

arXiv2024

Modulational instability in $\mathcal{PT}$-symmetric Bragg grating structures with four-wave mixing

We investigate the dynamics of modulational instability (MI) in $\cal PT$-symmetric fiber Bragg gratings with a phenomenon of intermodulation known as four-wave mixing (FWM). Although the impact of FWM has already been analyzed in the conventional systems, the inclusion of gain and loss, which induces the notion of $\cal PT$- symmetry, gives rise to many noteworthy outcomes. These include the manifestation of an unusual double-loop structure in the dispersion curve, which was unprecedented in the context of conventional periodic structures. When it comes to the study of MI, which is usually obtained in the system by imposing a small amount of perturbations on the continuous wave by executing linear stability analysis, different regimes which range from conventional to broken $\cal PT$- symmetry tend to create quite a few types of MI spectra. Among them, we observe a unique MI pattern that mimics a tilted two-conical structure facing opposite to each other. In addition, we also address the impact of other non-trivial system parameters, such as input power, gain and loss and self-phase modulation in two important broad domains, including normal and anomalous dispersion regimes under the three types of $\cal PT$- symmetric conditions in detail.

physics.optics↗

arXiv2024

Unique multistable states in periodic structures with saturable nonlinearity

We report that conventional saturable periodic structures, in sharp contrast to the conventional systems with different nonlinearities which exhibit the typical S- shaped optical bi- and multi-stable states, reveal some unusual and unique nonlinear dynamics. These include the onset of ramp-like optical bistability (OB) and optical multistability (OM) curves which further transit into mixed OM states combining both ramp-like states followed by the S-shaped multistable curves. We also extend this study to another domain of physics, namely parity-time ($\mathcal{PT}$)- symmetry, by including equal amount of gain and loss into the system which then establishes additional degree of freedom by enabling the investigation into additional two domains which are the unbroken and broken $\mathcal{PT}$- symmetric regimes. Although these bi- and multi-stable states are unusual and unique, when the frequency detuning is introduced, the revival of S-shaped stable states is possible but only in the presence of unbroken $\mathcal{PT}$- symmetry. Conversely, the broken $\mathcal{PT}$- symmetry which usually generates ramp-like multistable states, gives rise to the birth of novel multistable states with a vortex like envelope, (the curve that features simultaneous increase in the critical switch-up and switch-down powers with an increase in the input power) causing a novel structure which has not been reported in the existing literature of different physical systems manifesting multi-stable states.

physics.optics↗

arXiv2024

Reservoir computing with logistic map

Recent studies on reservoir computing essentially involve a high dimensional dynamical system as the reservoir, which transforms and stores the input as a higher dimensional state, for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely Lorenz, Rossler, and Hindmarsh-Rose, for temporal tasks and a seventh order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rossler system for the future (self prediction).

cond-mat.dis-nn↗

arXiv2024

Electromagnetic breathing dromion-like structures in an anisotropic ferromagnetic medium

The influence of Gilbert damping on the propagation of electromagnetic waves (EMWs) in an anisotropic ferromagnetic medium is investigated theoretically. The interaction of the magnetic field component of the electromagnetic wave with the magnetization of a ferromagnetic medium has been studied by solving the associated Maxwell's equations coupled with a Landau-Lifshitz-Gilbert (LLG) equation. When small perturbations are made on the magnetization of the ferromagnetic medium and magnetic field along the direction of propagation of electromagnetic wave by using the reductive perturbation method, the associated nonlinear dynamics is governed by a time-dependent damped derivative nonlinear Schrodinger (TDDNLS) equation. The Lagrangian density function is constructed by using the variational method to solve the TDDNLS equation to understand the dynamics of the system under consideration. The propagation of EMW in a ferromagnetic medium with inherent Gilbert damping admits very interesting nonlinear dynamical structures. These structures include Gilbert damping-managing symmetrically breathing solitons, localized erupting electromagnetic breathing dromion-like modes of excitations, breathing dromion-like soliton, decaying dromion-like modes and an unexpected creation-annihilation mode of excitations in the form of growing-decaying dromion-like modes.

nlin.PS↗

arXiv2024

Analytical solutions of higher-dimensional coupled system of nonlinear time-fractional diffusion-convection-wave equations

This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order derivative for the first time. Specifically, we describe how to systematically find different invariant product linear spaces with various dimensions for the considered system. Also, we observe that the obtained invariant product linear spaces help to reduce the multi-component (N+1)-dimensional coupled NTFPDEs into a system of fractional-order ODEs, which can then be solved using the well-known analytical methods. More precisely, we illustrate the effectiveness and importance of this developed method for obtaining a long list of invariant product linear spaces for the multi-component (2+1)-dimensional coupled nonlinear time-fractional diffusion-convection-wave equations. In addition, we have shown how to find different kinds of generalized separable analytical solutions for a multi-component (2 + 1)-dimensional coupled nonlinear time-fractional diffusion-convection-wave equations along with the initial and boundary conditions using invariant product linear spaces obtained. Finally, we provide appropriate graphical representations of some of the derived generalized separable analytical solutions with various fractional-order values.

math.AP↗

arXiv2024

On the solutions of coupled nonlinear time-fractional diffusion-reaction system with time delays

In this article, we systematically explain how to apply the analytical technique called the invariant subspace method to find various types of analytical solutions for a coupled nonlinear time-fractional system of partial differential equations with time delays. Also, the present work explicitly studies a systematic way to obtain various kinds of finite-dimensional invariant vector spaces for the coupled nonlinear time-fractional diffusion-reaction (DR) system with time delays under the two distinct fractional derivatives, namely (a) the Riemann-Liouville fractional partial time derivative and (b) the Caputo fractional partial time derivative. Additionally, we provide details of deriving analytical solutions in the generalized separable form for the initial and boundary value problems (IBVPs) of the coupled nonlinear time-fractional DR system with multiple time delays through the obtained invariant vector spaces under the considered two time-fractional derivatives.

math.AP↗

arXiv2024

Nonlinear two-component system of time-fractional PDEs in (2+1)-dimensions: Invariant subspace method combined with variable transformation

In this article, we develop a systematic approach of the invariant subspace method combined with variable transformation to find the generalized separable exact solutions of the nonlinear two-component system of time-fractional PDEs (TFPDEs) in (2+1)-dimensions for the first time. Also, we explicitly explain how to construct various kinds of finite-dimensional invariant linear product spaces for the given system using the invariant subspace method combined with variable transformation. Additionally, we present how to use the obtained invariant linear product spaces to derive the generalized separable exact solutions of the discussed system. We also note that the discussed method will help to reduce the nonlinear two-component system of TFPDEs in (2+1)-dimensions into the nonlinear two-component system of TFPDEs in (1+1)-dimensions, which again reduces to a system of time-fractional ODEs through the obtained invariant linear product spaces. More specifically, the significance and efficacy of the systematic investigation of the discussed method have been investigated through the initial and boundary value problems of the generalized nonlinear two-component system of time-fractional reaction-diffusion equations (TFRDEs) in (2+1)-dimensions for finding the generalized separable exact solutions, which can be expressed in terms of the exponential, trigonometric, polynomial, Euler-Gamma and Mittag-Leffler functions. Also, 2D and 3D graphical representations of some of the obtained solutions are presented for different values of fractional orders.

nlin.SI↗

arXiv2024

Unique multistable states in periodic structures with saturable nonlinearity. II. Broken $\mathcal{PT}$-symmetric regime

In this work, we observe that the $\mathcal{PT}$-symmetric fiber Bragg gratings (PTFBGs) with saturable nonlinearity (SNL) exhibit ramp-like, mixed, optical multistability (OM) in the broken regime. The interplay between nonlinearity and detuning parameter plays a central role in transforming the characteristics of the hysteresis curves and facilitates the realization of different OM curves. Also, it plays a crucial role in reducing the switch-up and down intensities of various stable branches of an OM curve. In a mixed OM curve, either the ramp-like hysteresis curves or S-like hysteresis curves can appear predominantly depending on the magnitude of the detuning parameter. An increase in the device length or nonlinearity increases the number of stable states for fixed values of input intensity. Under a reversal in the direction of light incidence, the ramp-like OM and mixed OM curves assume an unusual vortex-like envelope at lower intensities. Numerical simulations reveal that the switch-up and down intensities of different stable branches of a ramp-like OM and mixed OM curves drift towards the higher and lower intensity sides, respectively (opposite direction). The drift is severe to the extent that an intermediate hysteresis curve features switch-down action at near-zero switching intensities. Also, the input intensities required to realize ramp-like, and mixed OM curves reduce dramatically under a reversal in the direction of light incidence.

physics.optics↗

arXiv2024

Unique multistable states in periodic structures with saturable nonlinearity. I. Conventional case and unbroken $\mathcal{PT}$-symmetric regime

In this work, we predict that periodic structures without gain and loss do not exhibit an S-shaped hysteresis curve in the presence of saturable nonlinearity (SNL). Instead, the input-output characteristics of the system admit ramp-like optical bistability (OB) and multistability (OM) curves that are unprecedented in the context of conventional periodic structures in the literature. An increase in the nonlinearity (NL) or the gain-loss parameter increases the switch-up and down intensities of different stable branches in a ramp-like OM curve. Revival of the typical S-shaped hysteresis curve requires the device to work under the combined influence of frequency detuning and $\mathcal{PT}$-symmetry. An increase in the detuning, NL and gain-loss parameters reduces the switching intensities of the S-shaped OB (OM) curves. During the process, mixed OM curves that feature a fusion between ramp-like and S-shaped OM curves emanate at low values of the detuning parameter in the input-output characteristics. The detuning parameter values for which ramp-like, S-shaped, and mixed OM appear varies with the NL coefficient. For a given range of input intensities, the number of stable states admitted by the system increases with the device length or NL. When the laser light enters the device from the opposite end of the grating, nonreciprocal switching occurs at ultra-low intensities via an interplay between NL, detuning, and gain-loss parameters.

physics.optics↗