Soliton Solutions of a Coupled Modified KdV Equations

Iwao, Masataka; Hirota, Ryogo

doi:10.1143/jpsj.66.577

Cited by 84 publications

(52 citation statements)

References 3 publications

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“…The remaining problem is to construct the matrix S by virtue of the solutions of the linear eigenvalue problems (4). However, there are reduction (9) and constraints among elements in Q and the Darboux transformation should keep the reduction and those constraints. Therefore, it is not easy to treat the reduced problem.…”

Section: The Darboux Transformation Of System (3)mentioning

confidence: 99%

Darboux Transformation and Symbolic Computation on Multi-Soliton and Periodic Solutions for Multi-Component Nonlinear Schr¨odinger Equations in an Isotropic Medium

Zhang

et al. 2009

Zeitschrift Für Naturforschung A

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The Darboux transformation is applied to a multi-component nonlinear Schrödinger system, which governs the propagation of polarized optical waves in an isotropic medium. Based on the Lax pair associated with this integrable system, the formula for the n-times iterative Darboux transformation is constructed in the form of block matrices. The purely algebraic iterative algorithm is carried out via symbolic computation, and two different kinds of solutions of practical interest, i. e., bright multi-soliton solutions and periodic solutions, are also presented according to the zero and nonzero backgrounds.

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Section: The Darboux Transformation Of System (3)mentioning

confidence: 99%

Darboux Transformation and Symbolic Computation on Multi-Soliton and Periodic Solutions for Multi-Component Nonlinear Schr¨odinger Equations in an Isotropic Medium

Zhang

et al. 2009

Zeitschrift Für Naturforschung A

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“…Generalization of the mKdV equation to a multicomponent system or matrix equation was studied in [13]. Relatively recently, Iwao and Hirota [14] discussed a simple coupled version of the mKdV equation or the so-called coupled mKdV equation…”

Section: Introductionmentioning

confidence: 99%

On complexly coupled modified KdV equations

Choudhuri

2010

Pramana - J Phys

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We introduced complexly coupled modified KdV (ccmKdV) equations, which could be derived from a two-layer fluid model [Yang and Mao, Chin. Phys. Lett. 25, 1527 (2008); Hu, J. Phys. A: Math. Theor. 43, 185207 (2009)], and used the Miura transformation to construct expressions for their alternative Lax pair representations. We derived a Lagrangian-based approach to study the Hamiltonian structures of the ccmKdV equations and observed that the complexly coupled mKdV equations have an additional analytic structure. The coupled equations were characterized by two alternative Lagrangians not connected by a gauge term. We examined how the alternative Lagrangian descriptions of the system affect the bi-Hamiltonian structures.

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“…A coupled modified KdV equation is obtained by considering the following coupled form of the modified KdV equations [4].…”

Section: Introduction a Pfaffian Is The Square Root Of An Anti-symmementioning

confidence: 99%

Soliton equations exhibiting Pfaffian solutions

Hirota¹,

Iwao²,

Tsujimoto³

2001

Glasgow Math. J.

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Soliton Solutions of a Coupled Modified KdV Equations

Cited by 84 publications

References 3 publications

Darboux Transformation and Symbolic Computation on Multi-Soliton and Periodic Solutions for Multi-Component Nonlinear Schr¨odinger Equations in an Isotropic Medium

Darboux Transformation and Symbolic Computation on Multi-Soliton and Periodic Solutions for Multi-Component Nonlinear Schr¨odinger Equations in an Isotropic Medium

On complexly coupled modified KdV equations

Soliton equations exhibiting Pfaffian solutions

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