Coalescence of Wavenumbers and Exact Solutions for a System of Coupled Nonlinear Schrödinger Equations

Chow, K. W.; Lai, Derek W. C.

doi:10.1143/jpsj.67.3721

Cited by 18 publications

(8 citation statements)

References 11 publications

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“…One can also check that the above general three-soliton solution of the 2-CNLS equations reduces to that of the solution given in Ref. [24] for the particular case α (1) 3 = 1. Further, the form in which we have presented the solution eases the complexity in generalizing the solution to multicomponent case as well as to higher order soliton soutions.…”

Section: Three-soliton Solutionmentioning

confidence: 69%

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

2003

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The different dynamical features underlying soliton interactions in coupled nonlinear Schrödinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (up to four-soliton solutions) for two-coupled and arbitrary N-coupled nonlinear Schrödinger 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 pairwise 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 at least one soliton during interactions of more than two solitons represented by three- and higher-order soliton solutions. From an 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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Section: Three-soliton Solutionmentioning

confidence: 69%

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

2003

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“…a singular limit of two nearly equal wavenumbers. 20) Consequently, even though the merging of poles formulations have not yet been fully worked out for eq.…”

Section: The Double Pole Solutionmentioning

confidence: 99%

“…19) Mathematically, this is accomplished by taking a singular limit for solitary modes with nearly identical wavenumbers, augmented by special phase factors, and thus an appropriate name might be a 'coalescence of wavenumbers'. 20,21) Alternatively these results can also be derived in terms of a 'double pole' (or 'multiple pole') solution in the language of the inverse scattering transform, 22,23) where a double pole in the reflection coefficient also leads to these exponentialalgebraic modes. If these procedures are performed in the long wave regime (wavenumber tending to zero), one recovers these rogue waves / purely algebraic modes.…”

Section: Introductionmentioning

confidence: 99%

Rogue Wave Modes for the Long Wave–Short Wave Resonance Model

et al. 2013

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The long wave-short wave resonance model arises physically when the phase velocity of a long wave matches the group velocity of a short wave. It is a 2 system of nonlinear evolution equations solvable by the Hirota bilinear method and also possesses a Lax pair formulation. 'Rogue wave' modes, algebraically localized entities in both space and time, are constructed from the breathers by a singular limit involving a 'coalescence' of wavenumbers in the long wave regime. In contrast with the extensively studied nonlinear Schrödinger case, the frequency of the breather cannot be real and must satisfy a cubic equation with complex coefficients. The same limiting procedure applied to the finite wavenumber regime will yield mixed exponential-algebraic solitary waves, similar to the classical 'double pole' solutions of other evolution systems.

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“…Furthermore, such solutions can be derived by the coalescence of wavenumbers in the two-soliton solutions [35].…”

Section: Double-pole Solutionmentioning

confidence: 99%

Breather and double-pole solutions of the derivative nonlinear Schrödinger equation from optical fibers

Xiao

Liu

et al. 2011

Physics Letters A

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Coalescence of Wavenumbers and Exact Solutions for a System of Coupled Nonlinear Schrödinger Equations

Cited by 18 publications

References 11 publications

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

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

Rogue Wave Modes for the Long Wave–Short Wave Resonance Model

Breather and double-pole solutions of the derivative nonlinear Schrödinger equation from optical fibers

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