The Coupled Modified Korteweg-de Vries Equations
The Coupled Modified Korteweg-de Vries Equations
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DOI：
10.1143/jpsj.67.1175
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发表时间：
1998-04
影响因子：
1.7
通讯作者：
T. Tsuchida;M. Wadati
中科院分区：
文献类型：
--
作者：
T. Tsuchida;M. Wadati
将修正的KdV方程推广到一个多组分体系，即\（\frac{\partial u_i}{\partial t} + 6 \bigl（\sum_{j，k=0}^{M-1} C_{jk} u_j u_k \bigr）\frac{\partial x} + \frac{\partial^3 u_{i}}{\partial x^3} =0\），i =0，1，...，M-1.我们应用一个新的扩展版本的逆散射方法，这个系统。结果表明，该系统具有无穷多个守恒律和多孤子解。进一步解决了模型的初值问题。
Generalization of the modified KdV equation to a multi-component system, that is expressed by \(\frac{\partial u_i}{\partial t} + 6 \bigl( \sum_{j,k=0}^{M-1} C_{jk} u_j u_k \bigr) \frac{\partial u_i}{\partial x} + \frac{\partial^3 u_{i}}{\partial x^3} =0\), 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.