The Coupled Modified Korteweg-de Vries Equations

Details The Coupled Modified Korteweg-de Vries Equations The Coupled Modified Korteweg-de Vries Equations

1998-12-03

arxiv.org/abs/solv-int/9812003v1

J. Phys. Soc. Jpn. 67 (1998) 1175-1187

Nonlinear Sciences

Exactly Solvable and Integrable Systems

26 pages, LaTex209 file, uses jpsj.sty

Scientific paper

10.1143/JPSJ.67.1175

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.

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