arXiv subjects

M. Lakshmanan

Publications and source records attributed to M. Lakshmanan.

At least 37 records · Page 2Linked to original sources

arXiv2024

Painlevé Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped Hénon-Heiles System

We consider a modified damped version of Hénon-Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that the modified Hénon-Heiles system possesses the Painlevé property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle-Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified Hénon-Heiles system. We infer that the modified Hénon-Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases.

nlin.SI↗

arXiv2024

Coupled Nonlinear Schrödinger System: Role of Four-Wave Mixing Effect on Nondegenerate Vector Solitons

In this paper, we investigate the role of four-wave mixing effect on the structure of nondegenerate vector solitons and their collision dynamics. For this purpose, we consider the generalized coupled nonlinear Schrödinger (GCNLS) system which describes the evolution and nonlinear interaction of the two optical modes. The fundamental as well as higher-order nondegenerate vector soliton solutions are derived through the Hirota bilinear method and their forms are rewritten in a compact way using Gram determinants. Very interestingly, we find that the presence of four-wave mixing effect induces a breathing vector soliton state in both the optical modes. Such breather formation is not possible in the fundamental vector bright solitons of the Manakov system. Then, for both strong and weak four-wave mixing effects, we show that the nondegenerate solitons in the GCNLS system undergo, in general, novel shape changing collisions, in addition to shape preserving collision under suitable choice of wave numbers. Further, we analyze the degenerate soliton collision induced novel shape changing property of nondegenerate vector soliton by deriving the partially nondegenerate two-soliton solution. For completeness, the various collision scenarios related to the pure degenerate bright solitons are indicated. We believe that the results reported in this paper will be useful in nonlinear optics for manipulating light by light through collision.

nlin.PS↗

arXiv2023

Harnessing vibrational resonance to identify and enhance input signals

We report the occurrence of vibrational resonance (VR) and the underlying mechanism in a simple piecewise linear electronic circuit, namely the Murali-Lakshmanan-Chua (MLC) circuit, driven by an additional biharmonic signal with widely different frequency. When the amplitude of the high-frequency force is tuned, the resultant vibrational resonance is used to detect the low-frequency signal and also to enhance it into a high-frequency signal. Further, we also show that even when the low-frequency signal is changed from sine wave to square and sawtooth waves, vibrational resonance can be used to detect and enhance them into high-frequency signals. These behaviors, confirmed by experimental results, are illustrated with appropriate analytical and numerical solutions of the corresponding circuit equations describing the system. Finally, we also verify the signal detection in the above circuit even with the addition of noise.

nlin.AO↗

arXiv2023

Soliton molecules in Fermi-Pasta-Ulam-Tsingou lattice: Gardner equation approach

We revisit the Fermi-Pasta-Ulam-Tsingou lattice (FPUT) with quadratic and cubic nonlinear interactions in the continuous limit by deducing the Gardner equation. Through the Hirota bilinear method, multi-soliton solutions are obtained for the Gardner equation. Based on these solutions, we show the excitation of an interesting class of table-top soliton molecules in the FPUT lattice through the velocity resonance mechanism. Depending on the condition on the free parameters, we classify them as dissociated and synthetic type molecules. The main feature of the table-top soliton molecules is that they do not exhibit oscillations in the coalescence region. This property ensures that they are distinct from the soliton molecules, having retrieval force, of the nonlinear Schrödinger family of systems. Further, to study the stability of the soliton molecule we allow it to interact with a single (or multi) soliton(s). The asymptotic analysis shows that their structures remain constant, though the bond length varies, throughout the collision process. In addition, we consider the FPUT lattice with quadratic nonlinear interaction and FPUT lattice with cubic nonlinearity as sub-cases and point out the nature of the soliton molecules for these cases also systematically. We achieve this based on the interconnections between the solutions of the Gardner, modified K-dV and K-dV equations. Finally, we simulate the FPUT chain corresponding to the Gardner equation numerically and verify the existence of all the soliton structures associated with it. We believe that the present study can be extended to other integrable and non-integrable systems with applications in fluid dynamics, Bose-Einstein condensates, nonlinear optics, and plasma physics.

nlin.PS↗

arXiv2023

Exploration of field-like torque and field-angle tunability in coupled spin-torque nano oscillators for synchronization

We investigate the influence of field-like torque and the direction of the external magnetic field on a one-dimensional array of serially connected spin-torque nano oscillators, having free layers with perpendicular anisotropy, to achieve complete synchronization between them by analyzing the associated Landau-Lifshitz-Gilbert-Slonczewski equation. The obtained results for synchronization are discussed for the cases of 2, 10 and 100 oscillators separately. The roles of the field-like torque and the direction of the external field on the synchronization of the STNOs are explored through the Kuramoto order parameter. While the field-like torque alone is sufficient to bring out global synchronization in the system made up of a small number of STNOs, the direction of the external field is also needed to be slightly tuned to synchronize the one-dimensional array of a large number of STNOs. The formation of complete synchronization through the construction of clusters within the system is identified for the 100 oscillators. The large amplitude synchronized oscillations are obtained for small to large numbers of oscillators. Moreover, the tunability in frequency for a wide range of currents is shown for the synchronized oscillations up to 100 spin-torque oscillators. In addition to achieving synchronization, the field-like torque increases the frequency of the synchronized oscillations. The transverse Lyapunov exponents are deduced to confirm the stable synchronization in coupled STNOs due to the field-like torque and to validate the results obtained in the numerical simulations. The output power of the array is estimated to be enhanced substantially due to complete synchronization by the combined effect of field-like torque and tunability of the field angle.

cond-mat.mes-hall↗

arXiv2023

Simulation of universal optical logic gates under energy sharing collisions of Manakov solitons and fulfillment of practical optical logic criteria

The universal optical logic gates, namely NAND and NOR gates, have been theoretically simulated by employing the energy sharing collision of bright optical solitons in the Manakov system, governing pulse propagation in a highly birefringent fiber. Further, we also realize the two input optical logic gates such as AND, OR, XOR, XNOR for completeness of our scheme. Interestingly, our idea behind the simulation naturally satisfies all the criteria for practical optical logic which in turn displays the strength and versatility of our theoretical simulation of universal optical logic gates. Hence, our approach paves the way for the experimentalists to create a new avenue in this direction if the energy sharing collisions of Manakov solitons are experimentally realized in the future.

nlin.SI↗

arXiv2023

Shear induced symmetry breaking dynamical states

We examine how shear influences the emergence of symmetry-breaking dynamical states in a globally coupled Stuart-Landau (SL) oscillator system with combined attractive and repulsive interactions. In the absence of the shear parameter, the system exhibits synchronization, nontrivial oscillation death states, and oscillation death states. However, with the introduction of the shear parameter, we observe diverse dynamical patterns, including amplitude clusters, solitary states, complete synchronization, and nontrivial oscillation death states when the repulsive interaction is weak. As the strength of the repulsive interaction increases, the system becomes more heterogeneous, resulting in imperfect solitary states. We also validate the analytical stability condition for the oscillation death region and compare it with the numerical boundary, finding a close match. Furthermore, we discover that the presence of shear leads to the emergence of symmetry-breaking dynamical states, specifically inhomogeneous oscillation death states and oscillatory cluster states under nonlocal coupling interaction.

nlin.AO↗

arXiv2023

High frequency oscillations in spin-torque nano oscillator due to bilinear coupling

Exchange coupling in an interfacial context is crucial for spin-torque nano oscillator (STNO) that consists of a non-magnetic spacer which is alloyed with a ferromagnetic material. Currently, investigations on the dynamics of the free layer magnetization and frequency enhancement in the STNO with bilinear coupling are still being actively pursued. In the present work, we investigate the dynamics of the STNO in the presence of bilinear coupling but in the absence of an external magnetic field by analyzing the associated Landau-Lifshitz-Gilbert-Sloncewski(LLGS) equation, and consequently the impact of the bilinear coupling on the dynamics of the magnetization of the free layer is studied. It is observed that the frequency of the oscillations in the magnetization component along the direction of the pinned layer polarization can be enhanced above 300 GHz by positive bilinear coupling and up to around 30 GHz by negative bilinear coupling. We further reveal a transition from in-plane to out-of-plane precession both for positive and negative bi-linear couplings. We also analyze the switching of the magnetization for different values of current and bilinear coupling. Our detailed investigations of STNO with bilinear coupling aim at the possibilities of high-frequency devices by considering the applied current and bilinear coupling in the absence of a magnetic field.

cond-mat.mes-hall↗

arXiv2023

Invariant subspace method for (m + 1)-dimensional non-linear time-fractional partial differential equations

In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method have been systematically investigated through the (3 + 1)-dimensional generalized non-linear time-fractional diffusion-convection-wave equation along with appropriate initial conditions. This systematic investigation provides an important technique to find a large class of various types of the invariant subspaces with different dimensions for the above-mentioned equation. Additionally, we have shown that the obtained invariant subspaces help to derive a variety of exact solutions that can be expressed as the combinations of exponential, trigonometric, polynomial and well-known Mittag-Leffler functions.

nlin.SI↗

arXiv2023

Invariant subspace method to the initial and boundary value problem of the higher dimensional nonlinear time-fractional PDEs

This paper systematically explains how to apply the invariant subspace method using variable transformation for finding the exact solutions of the (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown how to transform the given (k+1)-dimensional nonlinear time-fractional PDEs into (1+1)-dimensional nonlinear time-fractional PDEs using the variable transformation procedure. Also, we explain how to derive the exact solutions for the reduced equations using the invariant subspace method. Additionally, in this careful and systematic study, we will investigate how to find the various types of exact solutions of the (3+1)-dimensional nonlinear time-fractional convection-diffusion-reaction equation along with appropriate initial and boundary conditions for the first time. Moreover, the obtained exact solutions of the equation as mentioned above can be written in terms of polynomial, exponential, trigonometric, hyperbolic, and Mittag-Leffler functions. Finally, the discussed method is extended for the (k+1)-dimensional nonlinear time-fractional PDEs with several linear time delays, and the exact solution of the (3+1)-dimensional nonlinear time-fractional delay convection-diffusion-reaction equation is derived.

nlin.SI↗

arXiv2023

Modulational instability in $\cal{PT}$-symmetric Bragg grating structures with saturable nonlinearity

We investigate the nontrivial characteristics of modulational instability (MI) in a system of Bragg gratings with saturable nonlinearity. We also introduce an equal amount of gain and loss into the existing system which gives rise to an additional degree of freedom, thanks to the concept of $\cal PT$- symmetry. We obtain the nonlinear dispersion relation of the saturable model and discover that such dispersion relations for both the conventional and $\cal PT$- symmetric cases contradict with the conventional Kerr and saturable systems by not displaying the typical signature of loop formation in either the upper branch or lower branch of the curve drawn against the wavenumber and detuning parameter. We then employ a standard linear stability analysis in order to study the MI dynamics of the continuous waves perturbed by an infinitesimal perturbation. The main objective of this paper is twofold. We first investigate the dynamics of the MI gain spectrum at the top and bottom of the photonic bandgap followed by a comprehensive analysis carried out in the anomalous and normal dispersion regimes. As a result, this perturbed system driven by the saturable nonlinearity and gain/loss yields a variety of instability spectra, which include the conventional side bands, monotonically increasing gain, the emergence of a single spectrum in either of the Stokes wavenumber region, and so on. In particular, we observe a remarkably peculiar spectrum, which is caused predominantly by the system parameter though the perturbation wavenumber boosts the former. We also address the impact of all the physical parameters considered in the proposed model which include coupling coefficient, dispersion parameter, and saturable nonlinearity on the phenomenon of MI for different $\cal PT$- symmetric regimes ranging from unbroken to broken one in greater detail.

nlin.PS↗

arXiv2023

Thermal quantum correlations and teleportation under PT-symmetric system

In this article, we exploit the different notions of quantumness measure to understand the properties of the Heisenberg XY model with and without PT-symmetric operation. In the absence of PT-symmetry, we study the significance of different measures, namely entanglement and measurement induced nonlocality (MIN), in the detection of the quantumness of the Heisenberg XY model. It is observed that the quantum correlations and teleportation fidelity monotonically decreases with respect to temperature. Furthermore, the intervention of PT-symmetric operation enhances the strengths of quantum correlation. In addition, we highlight the role of the system's parameters and PT-symmetric operation on the teleportation of a quantum state. Our results also emphasize that after the addition of PT-symmetric operation, the considered physical model remains a versatile resource to achieve successful teleportation of the quantum state.

quant-ph↗

arXiv2022

Additional complex conjugate feedback induced explosive death and multistabilities

Many natural and man-made systems require suitable feedback to function properly. In this study, we aim to investigate the impact of additional complex conjugate feedback on globally coupled Stuart-Landau oscillators. We find that this additional feedback results in the onset of symmetry breaking clusters and out-of-phase clusters. Interestingly, we also find the existence of explosive amplitude death along with disparate multistable states. We characterize the first-order transition to explosive death through the amplitude order parameter and show that the transition from oscillatory to death state indeed shows a hysteresis nature. Further, we map the global dynamical transitions in the parametric spaces. In addition, to understand the existence of multistabilities and their transitions, we analyze the bifurcation scenarios of the reduced model and also explore their basin stability. Our study will shed light on the emergent dynamics in the presence of additional feedback.

nlin.AO↗

arXiv2022

Analysis of COVID-19 in India using vaccine epidemic model incorporating vaccine effectiveness and herd immunity

COVID-19 will be a continuous threat to human population despite having a few vaccines at hand until we reach the endemic state through natural herd immunity and total immunization through universal vaccination. However, the vaccine acts as a practical tool for reducing the massive public health problem and the emerging economic consequences that the continuing COVID -19 epidemic is causing worldwide, while the vaccine efficacy wanes. In this work, we propose and analyze an epidemic model of Susceptible-Exposed-Infected-Recovered-Vaccinated (SEIRV) population taking into account the rate of vaccination and vaccine waning. The dynamics of the model has been investigated, and the condition for a disease-free endemic equilibrium state is obtained. Further, the analysis is extended to study the COVID-19 spread in India by considering the availability of vaccines and the related critical parameters such as vaccination rate, vaccine efficacy and waning of vaccine's impact on deciding the emerging fate of this epidemic. We have also discussed the conditions for herd immunity due to vaccinated individuals among the people. Our results highlight the importance of vaccines, the effectiveness of booster vaccination in protecting people from infection, and their importance in epidemic and pandemic modelling.

q-bio.PE↗

arXiv2022

Effect of interlayer exchange coupling in spin-torque nano oscillator

The dynamics of the magnetization of the free layer in a spin-torque nano oscillator (STNO) influenced by a noncollinear alignment between the magnetizations of the free and pinned layers due to an interlayer exchange coupling has been investigated theoretically. The orientations of the magnetization of the free layer with that of the pinned layer have been computed through the macrospin model and they are found to match well with experimental results. The bilinear and biquadratic coupling strengths make the current to switch the magnetization between two states or oscillate steadily. The expressions for the critical currents between which oscillations are possible and the critical bilinear coupling strength below which oscillations are not possible are derived. The frequency of the oscillations is shown to be tuned and increased to or above 300 GHz by the current which is the largest to date among nanopillar-shaped STNOs.

physics.app-ph↗

arXiv2022

Quantum solvability of a nonlinear $δ$-type mass profile system: Coupling constant quantization

In this paper, we discuss the quantum dynamics of a nonlinear system that admits temporally localized solutions at the classical level. We consider a general ordered position-dependent mass Hamiltonian in which the ordering parameters of the mass term are treated as arbitrary. The mass function here is singular at the origin. We observe that the quantum system admits bounded solutions but importantly the coupling parameter of the system gets quantized which has also been confirmed by the semiclassical study as well.

quant-ph↗

arXiv2022

Inhomogeneous nonlinearity meets $\mathcal{PT}$-symmetric Bragg structures: Route to ultra-low power steering and peculiar stable states

In the context of $\mathcal{PT}$-symmetric fiber Bragg gratings, tailoring the nonlinear profile along the propagation coordinate serves to be a new direction for realizing low-power all-optical switches. The scheme is fruitful only when the nonlinearity profile will be either linearly decreasing or increasing form. If the rate of variation of the nonlinearity profile is high, the critical intensities fall below the input power of value 0.01 in the unbroken regime provided that the light launching direction is right. Nowadays, every new theoretical inception into the PTFBG has started making sense of switching in the broken $\mathcal{PT}$-symmetric regime which was once believed to be the instability regime. When the inhomogeneous nonlinearity acts together with the broken $\mathcal{PT}$-symmetry and right light incidence, it leads to two peculiar settings. First, the switch-up intensities are ultra-low. Second, the switch-down action takes place at zero critical intensities. Such OB curves are unprecedented in the context of conventional gratings and found only in plasmonic devices and anti-directional couplers. Even though the nonlinearity is inhomogeneous, the ramp-like first stable states persist in the broken $\mathcal{PT}$-symmetric regime giving an additional indication that the broken PTFBG is closely associated with the plasmonic structures. In the existing PTFBG systems, the switching intensities are relatively higher in the broken regime. However, the proposed system records the lowest switching intensities in the broken regime. The reported intensities ($< 0.005$) are also the lowest ever-switching intensities recorded in the perspective of PTFBGs to date.

physics.optics↗

arXiv2022

Bright, dark and breather soliton solutions of the generalized long-wave short-wave resonance interaction system

In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid dynamics, plasma physics and nonlinear optics, is considered. Using the Hirota bilinear method, the general $N$-bright and $N$-dark soliton solutions are deduced and their Gram determinant forms are obtained. A special feature of the fundamental bright soliton solution is that, in general, it behaves like the Korteweg-deVries soliton. However, under a special condition, it also behaves akin to the nonlinear Schrödinger soliton when it loses the amplitude dependent velocity property. The fundamental dark-soliton solution admits anti-dark, grey, and completely black soliton profiles, in the short-wave component, depending on the choice of wave parameters. On the other hand, a bright soliton like profile always occurs in the long-wave component. The asymptotic analysis shows that both the bright and dark solitons undergo an elastic collision with a finite phase shift. In addition to these, by tuning the phase shift regime, we point out the existence of resonance interactions among the bright solitons. Furthermore, under a special velocity resonance condition, we bring out the various types of bright and dark soliton bound states. Also, by fixing the phase factor and the system parameter $β$, corresponding to the interaction between long and short wave components, the different types of profiles associated with the obtained breather solution are demonstrated.

nlin.PS↗