The Coupled Modified Korteweg-de Vries Equations

Abstract

Generalization of the modified KdV equation to a multi-component system, that is expressed by $(\partial u_i)/(\partial t)+6({\sum }_{j,k=0}^{M-1}{C}_{jk}{u}_j{u}_k)(\partial u_i)/(\partial x)+({\partial }^3{u}_i)/(\partial x^3)=0,i=0,1,...,M-1$, 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.

26 pages, LaTex209 file, uses jpsj.sty

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