The Coupled Modified Korteweg-de Vries Equations

1998/04/15 by Takayuki Tsuchida, T. Tsuchida, Miki Wadati +1 · 8 citations
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI #solv-int

paper · pdf · doi:10.1143/jpsj.67.1175

published as J. Phys. Soc. Jpn. 67 (1998) 1175-1187 · 26 pages, LaTex209 file, uses jpsj.sty

openalex publication_date 1998/04/15 · arxiv created 1998/12/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Generalization of the modified KdV equation to a multi-component system, that is expressed by (∂ u_i)/(∂ t) + 6 (∑_j,k=0^M-1 C_jk u_j u_k) (∂ u_i)/(∂ x) + (∂³ u_i)/(∂ x³) = 0, i=0, 1, ..., M-1 , is studied. We apply a new extended version of the inverse scattering method to this system. It is shown that this system has an infinite number of conservation laws and multi-soliton solutions. Further, the initial value problem of the model is solved.

Citations

• New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation

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