arXiv subjects

T. Kanna

Publications and source records attributed to T. Kanna.

At least 19 recordsLinked to original sources

arXiv2026

Multiple double-valley and single-valley dark solitons in the complex modified Korteweg-de Vries equation: shape-preserving collisions and shape-altering collisions

The shape-preserving and shape-altering collisions of dark solitons are investigated in the complex modified Korteweg-de Vries equation. The obtained dark soliton solutions are classified into two distinct types, referred to as type-I and type-II dark solitons, which exhibit fundamentally different structural and dynamical characteristics. A single type-I dark soliton is symmetric about its center and admits three distinct valley profiles, namely single-valley, double-valley, and flat-bottom structures, whereas a single type-II dark soliton only supports a single-valley profile. These two types of dark solitons differ in their phase behaviors as the spatial variable varies from $-\infty$ to $+\infty$, as well as in their velocity--amplitude relations. For multiple pure type-I dark solitons, collisions are shape-preserving; however, a nontrivial collective effect is revealed in which modifying the parameters of one soliton can induce changes in the profiles and amplitudes of the other solitons, even though all collisions remain elastic in nature. In contrast, multiple pure type-II dark solitons behave independently, undergoing only phase shifts without any modification of their shapes or amplitudes. When type-I and type-II dark solitons coexist, their interactions lead to genuine shape-altering collisions, where the valley structures and amplitudes of type-I dark solitons are modified, while type-II solitons remain unaffected except for phase shifts. Asymptotic analysis further shows that the influence of type-II dark solitons on type-I dark solitons is confined to the pre-collision stage and disappears after the interaction.

nlin.SI↗

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

Bright Matter-Wave Bound Soliton Molecules in Spin-1 Bose-Einstein Condensates with Non-autonomous Nonlinearities

This work deals with matter-wave bright soliton molecules in spin-1 Bose-Einstein condensates described by three-component Gross-Pitaevskii equations with non-autonomous nonlinearities that can be tuned by Feshbach resonance management. Notably, it portrays the possibility of generating bright bound soliton molecules with the help of an exact analytic solution under a controlled velocity resonance mechanism. Results show that these soliton molecules experience the effects of time-varying nonlinearities and modulate themselves during propagation by keeping their stable properties. Significantly, the chosen periodic and kink-like nonlinearities expose the snaking, bending, compression, and amplification of multi-structured soliton molecules along with appreciable changes in their amplitude, velocity, width, and oscillations of the molecule profiles. The present results will add significant knowledge to a complete understanding beyond the known interaction dynamics of matter-wave bright solitons in spinor condensates.

cond-mat.quant-gas↗

arXiv2020

Reviving Modulational Instability with Third-Order Dispersion

It is well-known that third-order dispersion (TOD) never allows the continuous wave of any nonlinear Schroedinger (NLS) type system to experience modulational instability (MI). Remarkably, we demonstrate a new kind of MI induced by TOD with spatial dispersion accounting for Wannier exciton mass in a ZnCdSe/ZnSe semiconductor superlattice. We also numerically predict the existence of novel Akhmediev breathers and Peregrine solitons due to the nonlinear development of MI with TOD.

nlin.PS↗

arXiv2020

Engineering Optical Rogue Waves and Breathers in a Coupled Nonlinear Schrödinger System with Four-Wave Mixing Effect

We consider a coherently coupled nonlinear Schrödinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium. By identifying an appropriate similarity transformation, we obtain a general localized wave solution and investigate their dynamics with a proper set of modulated nonlinearities. In particular, our study reveals different manifestations of localized waves such as stable solitons, Akhmediev breathers, Ma breathers, and rogue waves of bright, bright-dark, and dark-dark type and explores their manipulation mechanism with suitably engineered nonlinearity parameters. We have provided a categorical analysis with adequate graphical demonstrations.

nlin.PS↗

arXiv2020

Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schrödinger models with variable nonlinearities

We investigate non-autonomous solitons in a general coherently coupled nonlinear Schrödinger (CCNLS) system with temporally modulated nonlinearities and with an external harmonic oscillator potential. This general CCNLS system encompasses three distinct types of CCNLS equations that describe the dynamics of beam propagation in an inhomogeneous Kerr-like nonlinear optical medium for different choices of nonlinear polarizations owing to the anisotropy of the medium. We identify a generalized similarity transformation to relate the considered model into the standard integrable homogeneous coupled nonlinear evolution equations with constant nonlinearities, accompanied by a constraint relation expressed in the form of the Riccati equation. With the help of a non-standard Hirota's bilinearization method and exact soliton solutions, we explore the impact of varying nonlinearities and refractive index in the propagation and collisions analytically by reverse engineering. Interestingly, we show the emergence of several modulated solitonic phenomena such as periodic oscillation, amplification, compression, tunneling/cross-over, excitons, as well as their combined effect in the single-soliton propagation and two-soliton collisions with appropriate forms of nonlinearity. Notably, we identify a tool to transform the nature of soliton collisions with certain type of inhomogeneous nonlinearities. The results could be of significant interest to the studies on management of nonlinear waves in the contexts like nonlinear optics and can also be extended to Bose-Einstein condensates and super-fluids.

nlin.PS↗

arXiv2020

On the integrability aspects of nonparaxial nonlinear Schrödinger equation and the dynamics of solitary waves

The integrability nature of a nonparaxial nonlinear Schrödinger (NNLS) equation, describing the propagation of ultra-broad nonparaxial beams in a planar optical waveguide, is studied by employing the Painlevé singularity structure analysis. Our study shows that the NNLS equation fails to satisfy the Painlevé test. Nevertheless, we construct one bright solitary wave solution for the NNLS equation by using the Hirota's direct method. Also, we numerically demonstrate the stable propagation of the obtained bright solitary waves even in the presence of an external perturbation in a form of white noise. We then numerically investigate the coherent interaction dynamics of two and three bright solitary waves. Our study reveals interesting energy switching among the colliding solitary waves due to the nonparaxiality.

nlin.PS↗

arXiv2019

Spatially modulated two- and three-component Rabi-coupled Gross-Pitaevskii systems

Vector rogue wave (RW) formation and their dynamics in Rabi coupled two- and three-species Bose-Einstein condensates with spatially varying dispersion and nonlinearity are studied. For this purpose, we obtain the RW solution of the two- and three-component inhomogeneous Gross-Pitaevskii (GP) systems with Rabi coupling by introducing suitable rotational and similarity transformations. Then, we investigate the effect of inhomogeneity (spatially varying dispersion, trapping potential and nonlinearity) on vector RWs for two different forms of potential strengths, namely periodic (optical lattice) with specific reference to hyperbolic type potentials and parabolic cylinder potentials. First, we show an interesting oscillating boomeronic behaviour of dark-bright solitons due to Rabi coupling in two component-condensate with constant nonlinearities. Then in the presence of inhomogeneity but in the absence of Rabi coupling we demonstrate creation of new daughter RWs co-existing with dark (bright) soliton part in first (second) component of the two-component GP system. Further, the hyperbolic modulation (sech type) of parameter along with Rabi effect leads to the formation of dromion (two-dimensional localized structure) trains even in the (1+1) dimensional two-component GP system, which is a striking feature of Rabi coupling with spatial modulation. Next, our study on three-component condensate, reveals the fact that the three RWs can be converted into broad based zero background RW appearing on top of a bright soliton by introducing spatial modulation only. Further, by including Rabi coupling we observe beating behaviour of solitons with internal oscillations mostly at the wings. Also, we show that by employing parabolic cylinder modulation with model parameter $n$, one can produce $(n+1)$ RWs.

nlin.PS↗

arXiv2019

Cubic-quintic nonlinear Helmholtz equation: Modulational instability, chirped elliptic and solitary waves

We study the formation and propagation of chirped elliptic and solitary waves in cubic-quintic nonlinear Helmholtz (CQNLH) equation. This system describes nonparaxial pulse propagation in a planar waveguide with Kerr-like and quintic nonlinearities along with spatial dispersion originating from the nonparaxial effect that becomes dominant when the conventional slowly varying envelope approximation (SVEA) fails. We first carry out the modulational instability (MI) analysis of a plane wave in this system by employing the linear stability analysis and investigate the influence of different physical parameters on the MI gain spectra. In particular, we show the nonparaxial parameter suppresses the conventional MI gain spectrum and also leads to a nontrivial monotonic increase in the gain spectrum near the tails of the conventional MI band, a qualitatively distinct behaviour from the standard nonlinear Schrödinger (NLS) system. We then study the MI dynamics by direct numerical simulations which demonstrate production of ultra-short nonparaxial pulse trains with internal oscillations and slight distortions at the wings. Following the MI dynamics, we obtain exact elliptic and solitary wave solutions using the integration method by considering physically interesting chirped traveling wave ansatz. In particular, we show that the system features intriguing chirped anti-dark, bright, gray and dark solitary waves depending upon the nature of nonlinearities. We also show that the chirping is inversely proportional to the intensity of the optical wave. Especially, the bright and dark solitary waves exhibit unusual chirping behaviour which will have applications in nonlinear pulse compression process.

nlin.PS↗

arXiv2018

Harnessing energy sharing collisions of Manakov solitons to implement universal NOR and OR logic gates

The energy sharing collision of bright optical solitons in the Manakov system, governing pulse propagation in high birefringent fiber, is employed theoretically to realize optical logic gates. Especially, for the first time, we successfully construct (theoretically) the universal NOR gate and the OR gate from the energy sharing collisions of just four bright solitons which can be well described by the exact bright four-soliton solution of the Manakov system. This construction procedure has the important merits like realizing the two input gates with a minimal number of soliton collisions and possibilities of multi-state logic. The recent experiments on Manakov solitons suggest the possibility of implementation of this theoretical construction of such gates and ultimately an all optical computer.

nlin.PS↗

arXiv2018

Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation

We consider the nonlinear Helmholtz (NLH) equation describing the beam propagation in a planar waveguide with Kerr-like nonlinearity under non-paraxial approximation. By applying the Lie symmetry analysis, we determine the Lie point symmetries and the corresponding symmetry reductions in the form of ordinary differential equations (ODEs) with the help of the optimal systems of one-dimensional subalgebras. Our investigation reveals an important fact that in spite of the original NLH equation being non-integrable, its symmetry reductions are of Painlevé integrable. We study the resulting sets of nonlinear ODEs analytically either by constructing the integrals of motion using the modified Prelle-Singer method or by obtaining explicit travelling wave-like solutions including solitary and symbiotic solitary wave solutions. Also, we carry out a detailed numerical analysis of the reduced equations and obtain multi-peak nonlinear wave trains. As a special case of the NLH equation, we also make a comparison between the symmetries of the present NLH system and that of the standard nonlinear Schrödinger equation for which symmetries are long available in the literature.

nlin.SI↗

arXiv2017

A systematic construction of parity-time ($\cal PT$)-symmetric and non-$\cal PT$-symmetric complex potentials from the solutions of various real nonlinear evolution equations

We systematically construct a distinct class of complex potentials including parity-time ($\cal PT$) symmetric potentials for the stationary Schrödinger equation by using the soliton and periodic solutions of the four integrable real nonlinear evolution equations (NLEEs) namely the sine-Gordon (sG) equation, the modified Korteweg-de Vries (mKdV) equation, combined mKdV-sG equation and the Gardner equation. These potentials comprise of kink, breather, bion, elliptic bion, periodic and soliton potentials which are explicitly constructed from the various respective solutions of the NLEEs. We demonstrate the relevance between the identified complex potentials and the potential of the graphene model from an application point of view.

nlin.SI↗

arXiv2017

Non-autonomous bright solitons and their stability in Rabi coupled binary Bose-Einstein Condensates

The dynamics of non-autonomous bright matter-wave solitons in Rabi coupled binary Bose-Einstein condensates is explored. By performing a unitary and similarity/lens-type transformation, we reduce the non-autonomous Gross-Pitaevskii equation into the celebrated Manakov model. Then, we construct the exact bright solitons of the non-autonomous Gross-Pitaevskii system in the presence of time dependent nonlinearities for two specific forms, namely hyperbolic nonlinearities, which are of physical interest. The experimental possibilities of realizing the forms of temporally modulated potentials corresponding to these time dependent nonlinearities and supporting such localized structures are explored. Our study on the propagation of one soliton shows that the amplitude, velocity and shape of the bright soliton are altered by the time-dependent scattering length. We also analyse the non-trivial energy sharing collision of Manakov solitons in the presence of Rabi coupling and aforementioned nonlinearities. We find that breathers arise in two-soliton collisions and the nature of energy sharing collisions is altered from that of Manakov system due to Rabi coupling only. Further in the presence of time-dependent nonlinearities the collision scenario is again altered significantly. Finally, the stability of these localized structures is examined using a recently developed powerful analytic method by Quintero et. al., [Phys. Rev. E 91, 012905 (2015)] and it is shown that the non- autonomous bright solitons are indeed stable. The evolution of position and velocity is also studied.

nlin.PS↗

arXiv2016

Superposed nonlinear waves in coherently coupled Bose-Einstein condensates

We study the dynamics of superposed nonlinear waves in coherently coupled Gross-Pitaevskii (CCGP) equations with constant (autonomous system) and time varying (non-autonomous system) nonlinearity co-efficients. By employing a linear transformation, the autonomous CCGP system is converted into two separate scalar nonlinear Schrödinger equations and we show that linear superposition of different nonlinear wave solutions of these scalar equations results into several kinds of nonlinear coherent structures namely, coexisting rogue wave-Ma breather, Akhmediev-Ma breathers, collision and bound states of Ma breathers and solitons. Next, the non-autonomous CCGP system is converted into an autonomous CCGP system with a similarity transformation. We show an interesting possibility of soliton compression and appearance of creeping solitons for kink-like and periodically modulated nonlinearity coefficient.

nlin.PS↗

arXiv2015

Explicit construction of single input - single output logic gates from three soliton solution of Manakov system

We construct single input logic gates using the energy sharing collisions of a minimal number of (three) bright optical solitons associated with the three soliton solution of the integrable Manakov system. As computation requires state changes to represent binary logic, here we make use of the state change of a particular soliton during its sequential collision with other two solitons for constructing single input gates. As a consequence, we clearly demonstrate the construction of various one-input logic gates such as COPY gate, NOT gate and ONE gate using energy sharing three soliton collision of Manakov system. This type of realization of logic gates just from a three soliton collision (pair-wise interaction) is clearly distinct from the earlier studies which require separate collisions of four solitons.

nlin.SI↗

arXiv2015

Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations

We obtain a class of elliptic wave solutions of coupled nonlinear Helmholtz (CNLH) equations describing nonparaxial ultra-broad beam propagation in nonlinear Kerr-like media, in terms of the Jacobi elliptic functions and also discuss their limiting forms (hyperbolic solutions). Especially, we show the existence of non-trivial solitary wave profiles in the CNLH system. The effect of nonparaxiality on the speed, pulse width and amplitude of the nonlinear waves is analysed in detail. Particularly a mechanism for tuning the speed by altering the nonparaxial parameter is proposed. We also identify a novel phase-unlocking behaviour due to the presence of nonparaxial parameter.

nlin.PS↗

arXiv2014

Multicomponent long-wave--short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons

We consider a general multicomponent (2+1)-dimensional long-wave--short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long-wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multi-soliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.

nlin.SI↗

arXiv2014

Vector rogue waves and dark-bright boomeronic solitons in autonomous and non-autonomous settings

In this work, we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatio-temporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeron-like soliton solutions of the latter are converted back into ones of the original non-autonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.

nlin.PS↗