Integrable discretizations and soliton solution of KdV and mKdV equations

Zhang, Yi; Jin, Ligang; Dong, Kanghui

doi:10.1016/j.amc.2012.03.051

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…Recently, soliton solutions and Jordan-block solutions for the equation (1.2) [21] was derived through the generalized Cauchy matrix approach [22]. For the sd-mKdV equation (1.3), many approaches, such as inverse scattering transform [23,24], Darboux transformation [25,26], bilinear approach [27], discrete Jacobi sub-equation method [28], algebro-geometric approach [29], Riemann-Hilbert approach [30] and Deift-Zhou nonlinear steepest descent method [31], have been developed to construct its exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Rational solutions for three semi-discrete modified Korteweg–de Vries-type equations

Sun

Zhao

2019

Mod. Phys. Lett. B

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1 department of mathematics, university of shanghai for science and technology, shanghai, 200093, p.r. china 2 department of applied mathematics, zhejiang university of technology, hangzhou 310023, p.r. china Abstract. In this paper, we consider three semi-discrete modified Korteweg-de Vries type equations which are the nonlinear lumped self-dual network equation, the semi-discrete lattice potential modified Korteweg-de Vries equation and a semi-discrete modified Korteweg-de Vries equation. We derive several kinds of exact solutions, in particular rational solutions, in terms of the Casorati determinant for these three equations respectively. For some rational solutions, we present the related asymptotic analysis to understand their dynamics better.

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