The N-soliton solution of extended Korteweg-de Vries equation and SAR image simulation of internal solitary wave propagation

Zhang, Yuping; Nie, Xing-Xing; Wei, Guang-Mei; Liu, Ruiping

doi:10.1051/epjap/2014130358

Cited by 1 publication

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“…The classical nonlinear evolution equations (NLEEs) with soliton solutions, such as Korteweg-de Vries (KdV) equation and its extended equations, have been proposed to describe a variety of physical phenomena in the fields of hydrodynamics, ocean dynamics and plasma physics [1][2][3][4][5]. When the inhomogeneous media and the nonuniform boundaries are taken into account, the NLEEs with variable coefficient could describe nonlinear phenomena of the complex world more realistically than their constant-coefficient forms [6,7].…”

Section: Introductionmentioning

confidence: 99%

The Painlevé property, Bäcklund transformation, Lax pair and new analytic solutions of a generalized variable-coefficient KdV equation from fluids and plasmas

et al. 2015

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A generalized variable-coefficient Korteweg-de Vries (KdV) equation with variable-coefficients of x and t from fluids and plasmas is investigated in this paper. The explicit Painlevé-integrable conditions are given out by Painlevé test, and an auto-Bäcklund transformation is presented via the truncated Painlevé expansion. Under the integrable condition and auto-Bäcklund transformation, the analytic solutions are provided, including the soliton-like, periodic and rational solutions. Lax pair, Riccati-type auto-Bäcklund transformation (R-BT) and Wahlquist-Estabrook-type auto-Bäcklund transformation (WE-BT) are constructed in extended AKNS system. One-soliton-like and two-soliton-like solutions are obtained by R-BT and nonlinear superposition formula is obtained by WE-BT. The bilinear form and Nsoliton-like solutions are presented by Bell-polynomial approach. Based on the obtained analytic solutions, the propagation characteristics of waves effected by the variable coefficients are discussed.

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