The Prolongation Structure of a Coupled Kdv Equation

Jia, Yongxing; Duan, Wen-Shan

doi:10.1007/s10255-018-0741-2

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2019

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“…This method is one of the effective skills to verify whether the equation is integrable or not. The theory has been widely applied to many integrable equations, such as coupled KdV equation [32,33], coupled nonlinear Schröinger equation [34], and Heisenberg ferromagnet equation [35].…”

Section: Introductionmentioning

confidence: 99%

Prolongation Structures and N‐Soliton Solutions for a New Nonlinear Schrödinger‐Type Equation via Riemann‐Hilbert Approach

Lin

Fang

Dong

2019

Mathematical Problems in Engineering

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In this paper, a new integrable nonlinear Schrödinger-type (NLST) equation is investigated by prolongation structures theory and Riemann-Hilbert (R-H) approach. Via prolongation structures theory, the Lax pair of the NLST equation, a 2×2 matrix spectral problem, is derived. Depending on the analysis of red the spectral problem, a R-H problem of the NLST equation is formulated. Furthermore, through a specific R-H problem with the vanishing scattering coefficient, N-soliton solutions of the NLST equation are expressed explicitly. Moreover, a few key differences are presented, which exist in the implementation of the inverse scattering transform for NLST equation and cubic nonlinear Schrödinger (NLS) equation. Finally, the dynamic behaviors of soliton solutions are shown by selecting appropriate spectral parameter λ, respectively.

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