Jimbo-Miwa方程和Konopelchenko-Dubrovsky方程的解
Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations
摘要：
Jimbo-Miwa方程是著名的KP族可积系统中的第二个方程，它被用来描述物理学中某些有趣的（3+1）维波动，但没有通过任何常规的可积性检验。Konopelchenko-Dubrovsky方程在物理学中与具有弱色散的非线性编织有关。本文利用Xu的稳定域方法和我们对稳定域方法的对数推广，得到了这类方程的两族多参数函数的显式精确解.这些参数函数使我们的解更适用于相关的实际模型和边值问题。
英文摘要：
The Jimbo-Miwa equation is the second equation in the well known KP hierarchy of integrable systems, which is used to describe certain interesting (3+1)-dimensional waves in physics but not pass any of the conventional integrability tests. The Konopelchenko-Dubrovsky equations arose in physics in connection with the nonlinear weaves with a weak dispersion. In this paper, we obtain two families of explicit exact solutions with multiple parameter functions for these equations by using Xu's stable-range method and our logarithmic generalization of the stable-range method. These parameter functions make our solutions more applicable to related practical models and boundary value problems.
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