arXiv subjects

T. Kanna

Publications and source records attributed to T. Kanna.

34 records · Page 2Linked to original sources

arXiv2014

Mixed solitons in (2+1) dimensional multicomponent long-wave--short-wave system

We derive a (2+1)-dimensional multicomponent long-wave$-$short-wave resonance interaction (LSRI) system as the evolution equation for propagation of $N$-dispersive waves in weak Kerr type nonlinear medium in the small amplitude limit. The mixed (bright-dark) type soliton solutions of a particular (2+1)-dimensional multicomponent LSRI system, deduced from the general multicomponent higher dimensional LSRI system, are obtained by applying the Hirota's bilinearization method. Particularly, we show that the solitons in the LSRI system with two short-wave components behave like scalar solitons. We point out that for $N$-component LSRI system with $N>3$, if the bright solitons appear in atleast two components, interesting collision behaviour takes place resulting in energy exchange among the bright solitons. However the dark solitons undergo standard elastic collision accompanied by a position-shift and a phase-shift. Our analysis on the mixed bound solitons shows that the additional degree of freedom which arises due to the higher dimensional nature of the system results in a wide range of parameters for which the soliton collision can take place.

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arXiv2014

Elliptic Waves in Two Component Long Wave--Short Wave Resonance Interaction System in One and Two dimensions

We consider (2+1) and (1+1) dimensional long-wave short-wave resonance interaction systems. We construct an extensive set of exact periodic solutions of these systems in terms of Lamé polynomials of order one and two. The periodic solutions are classified into three categories as similar, mixed, superposed elliptic solutions. We also discuss the hyperbolic solutions as limiting cases.

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arXiv2014

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between one-dimensional long-wave and multiple short-waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative and mixed nonlinearity coefficients. We obtain general bright $N$-soliton solution of multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark and grey types, when the long-wave--short-wave resonance takes place. The short-wave component solitons undergo two types of energy sharing collisions. The solitons appearing in the long-wave component always exhibit elastic collision whereas that of short-wave components exhibit standard elastic collisions only for specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pair-wise nature of collision and unravel fascinating state restoration property.

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arXiv2013

Non-autonomous bright matter wave solitons in spinor Bose-Einstein condensates

We investigate the dynamics of bright matter wave solitons in spin-1 Bose-Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross-Pitaevskii (3-GP) equations using Hirota's method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite-Gaussian-like potential strength. Our study shows that these non-autonomous solitons undergo non-trivial collisions involving condensate switching.

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arXiv2013

Non-autonomous bright-dark solitons and Rabi oscillations in multi-component Bose-Einstein condensates

We study the dynamics of non-autonomous bright-dark matter-wave solitons in two- and three- component Bose-Einstein condensates. Our setting includes a time-dependent parabolic potential and scattering length, as well as Rabi coupling of the separate hyperfine states. By means of a similarity transformation, we transform the non-autonomous coupled Gross-Pitaevskii equations into the completely integrable Manakov model with defocusing nonlinearity, and construct the explicit form of the non-autonomous soliton solutions. The propagation characteristics for the one-soliton state, and collision scenarios for multiple soliton states are discussed in detail for two types of time-dependent nonlinearities: a kink-like one and a periodically modulated one, with appropriate time-dependence of the trapping potential. We find that in the two-component condensates the nature of soliton propagation is determined predominantly by the nature of the nonlinearity, as well as the temporal modulation of the harmonic potential; switching in this setting is essentially due to Rabi coupling. We also perform direct numerical simulation of the non-autonomous two-component coupled Gross-Pitaevskii equations to corroborate our analytical predictions. More interestingly, in the case of the three-component condensates, we find that the solitons can lead to collision-induced energy switching (energy-sharing collision), that can be profitably used to control Rabi switching or vice-versa. An interesting possibility of reversal of the nature of the constituent soliton, i.e., bright (dark) into dark (bright) due to Rabi coupling is demonstrated in the three-component setting.

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arXiv2011

Multicomponent coherently coupled and incoherently coupled solitons and their collisions

We consider the integrable multicomponent coherently coupled nonlinear Schrödinger (CCNLS) equations describing simultaneous propagation of multiple fields in Kerr type nonlinear media. The correct bilinear equations of $m$-CCNLS equations are obtained by using a non-standard type of Hirota's bilinearization method and the more general bright one solitons with single hump and double hump profiles including special flat-top profiles are obtained. The solitons are classified as coherently coupled solitons and incoherently coupled solitons depending upon the presence and absence of coherent nonlinearity arising due to the existence of the co-propagating modes/components. Further, by obtaining the more general two-soliton solutions using this non-standard bilinearization approach we demonstrate that the collision among coherently coupled soliton and incoherently coupled soliton displays a non-trivial collision behaviour in which the former always undergoes energy switching accompanied by an amplitude dependent phase-shift and change in the relative separation distance, leaving the latter unaltered. But the collision between coherently coupled solitons alone is found to be standard elastic collision. Our study also reveals the important fact that the collision between incoherently coupled solitons arising in the $m$-CCNLS system with $m=2$ is always elastic, whereas for $m>2$ the collision becomes intricate and for this case the $m$-CCNLS system exhibits interesting energy sharing collision of solitons characterized by intensity redistribution, amplitude dependent phase-shift and change in relative separation distance which is similar to that of the multicomponent Manakov soliton collisions. This suggests that the $m$-CCNLS system can also be a suitable candidate for soliton collision based optical computing in addition to the Manakov system.

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arXiv2010

Coherently coupled bright optical solitons and their collisions

We obtain explicit bright one- and two-soliton solutions of the integrable case of the coherently coupled nonlinear Schr{ö}dinger equations by applying a non-standard form of the Hirota's direct method. We find that the system admits both degenerate and non-degenerate solitons in which the latter can take single hump, double hump, and flat-top profiles. Our study on the collision dynamics of solitons in the integrable case shows that the collision among degenerate solitons and also the collision of non-degenerate solitons are always standard elastic collisions. But the collision of a degenerate soliton with a non-degenerate soliton induces switching in the latter leaving the former unaffected after collision, thereby showing a different mechanism from that of the Manakov system.

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arXiv2009

Painlev{é} singularity structure analysis of three component Gross-Pitaevskii type equations

In this paper, we have studied the integrability nature of a system of three coupled Gross-Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose-Einstein condensates by applying the Painlevé singularity structure analysis. We show that only for two sets of parametric choices, corresponding to the known integrable cases, the system passes the Painlevé test.

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arXiv2009

Higher dimensional bright solitons and their collisions in multicomponent long wave-short wave system

Bright plane soliton solutions of an integrable (2+1) dimensional ($n+1$)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one long wave component are found and then the results are generalized to the corresponding integrable ($n+1$)-wave system with $n$ short waves and single long wave. It is shown that the solitons in the short wave components (say $S^{(1)}$ and $S^{(2)}$) can be amplified by merely reducing the pulse width of the long wave component (say L). The study on the collision dynamics reveals the interesting behaviour that the solitons which split up in the short wave components undergo shape changing collisions with intensity redistribution and amplitude-dependent phase shifts. Even though similar type of collision is possible in (1+1) dimensional multicomponent integrable systems, to our knowledge for the first time we report this kind of collisions in (2+1) dimensions. However, solitons which appear in the long wave component exhibit only elastic collision though they undergo amplitude-dependent phase shifts.

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arXiv2007

Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schrödinger equations

Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{ö}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization method. Generally, for the mixed N-CNLS equations the bright and dark solitons can be split up in $(N-1)$ ways. By analysing the collision dynamics of these coupled bright and dark solitons systematically we point out that for $N>2$, if the bright solitons appear in at least two components, non-trivial effects like onset of intensity redistribution, amplitude dependent phase-shift and change in relative separation distance take place in the bright solitons during collision. However their counterparts, the dark solitons, undergo elastic collision but experience the same amplitude dependent phase-shift as that of bright solitons. Thus in the mixed CNLS system there co-exist shape changing collision of bright solitons and elastic collision of dark solitons with amplitude dependent phase-shift, thereby influencing each other mutually in an intricate way.

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arXiv2007

Periodic energy switching of bright solitons in mixed coupled nonlinear Schr{ö}dinger equations with linear self and cross coupling terms

The bright soliton solutions of the mixed 2-coupled nonlinear Schr{ö}dinger (CNLS) equations with linear self and cross coupling terms have been obtained by identifying a transformation that transforms the corresponding equation to the integrable mixed 2-CNLS equations. The study on the collision dynamics of bright solitons shows that there exists periodic energy switching, due to the coupling terms. This periodic energy switching can be controlled by the new type of shape changing collisions of bright solitons arising in mixed 2-CNLS system, characterized by intensity redistribution, amplitude dependent phase shift and relative separation distance. We also point out that this system exhibits large periodic intensity switching even with very small linear self coupling strengths.

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arXiv2005

Shape changing (intensity redistribution) collisions of solitons in mixed coupled nonlinear Schr{ö}dinger equations

A novel kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable $N$-coupled nonlinear Schr{ö}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients. The corresponding soliton solutions for N=2 case are obtained by using Hirota's bilinearization method. The distinguishing feature of the mixed sign CNLS equations is that the soliton solutions can both be singular and regular. Although the general soliton solution admits singularities we present parametric conditions for which non-singular soliton propagation can occur. The multisoliton solutions and a generalization of the results to multicomponent case with arbitrary $N$ are also presented. An appealing feature of soliton collision in the present case is that all the components of a soliton can simultaneously enhance their amplitudes, which can lead to new kind of amplification process without induced noise.

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arXiv2003

Exact soliton solutions of coupled nonlinear Schrödinger equations: Shape changing collisions, logic gates and partially coherent solitons

The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{ö}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (upto four-soliton solutions) for two coupled and arbitrary $N$-coupled nonlinear Schr{ö}dinger equations using the Hirota bilinearization method, we bring out clearly the various features underlying the fascinating shape changing (intensity redistribution) collisions of solitons, including changes in amplitudes, phases and relative separation distances, and the very many possibilities of energy redistributions among the modes of solitons. However in this multisoliton collision process the pair-wise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons. Detailed asymptotic analysis also shows that when solitons undergo multiple collisions, there exists the exciting possibility of shape restoration of atleast one soliton during interactions of more than two solitons represented by three and higher order soliton solutions. From application point of view, we have shown from the asymptotic expressions how the amplitude (intensity) redistribution can be written as a generalized linear fractional transformation for the $N$-component case. Also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters, leading to possible multistate logic. In addition, we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape changing collisions, thereby explaining their variable profile and shape variation in collision process.

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arXiv2002

Effect of Phase Shift in Shape Changing Collision of Solitons in Coupled Nonlinear Schroedinger Equations

Soliton interactions in systems modelled by coupled nonlinear Schroedinger (CNLS) equations and encountered in phenomena such as wave propagation in optical fibers and photorefractive media possess unusual features : shape changing intensity redistributions, amplitude dependent phase shifts and relative separation distances. We demonstrate these properties in the case of integrable 2-CNLS equations. As a simple example, we consider the stationary two-soliton solution which is equivalent to the so-called partially coherent soliton (PCS) solution discussed much in the recent literature.

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arXiv2001

Shape-changing Collisions of Coupled Bright Solitons in Birefringent Optical Fibers

Wecritically review the recent progress in understanding soliton propagation in birefringent optical fibers.By constructing the most general bright two-soliton solution of the integrable coupled nonlinear Schroedinger equation (Manakov model) we point out that solitons in birefringent fibers can in general change their shape after interaction due to a change in the intensity distribution among the modes even though the total energy is conserved. However, the standard shape-preserving collision (elastic collision) property of the (1+1)-dimensional solitons is recovered when restrictions are imposed on some of the soliton parameters. As a consequence the following further properties can be deduced using this shape-changing collision. (i) The exciting possibility of switching of solitons between orthogonally polarized modes of the birefringent fiber exists. (ii) When additional effects due to periodic rotation of birefringence axes are considered, the shape changing collision can be used as a switch to suppress or to enhance the periodic intensity exchange between the orthogonally polarized modes. (iii) For ultra short optical soliton pulse propagation in non-Kerr media, from the governing equation an integrable system of coupled nonlinear Schroedinger equation with cubic-quintic terms is identified. It admits a nonlocal Poisson bracket structure. (iv) If we take the higher-order terms in the coupled nonlinear Schroedinger equation into account then their effect on the shape-changing collision of solitons, during optical pulse propagation, can be studied by using a direct perturbational approach.

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arXiv2001

Exact soliton solutions, shape changing collisions and partially coherent solitons in coupled nonlinear Schroedinger equations

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schroedinger equations (N-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyse the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partial coherent solitons (PCS) discussed in the literature are special cases of the higher order bright soliton solutions of the N-CNLS equations.

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