与二阶多项式等谱问题相联系的方程簇的Hirota双线性型

Bilinear Forms of the Equation Hiearchy Related to Polynomial Isospectrum Problem

利用 Hirota方法可直接求出非线性发展方程的孤立子解 ,此方法首要是通过一个变换将非线性发展方程约化为新的方程 ,即所谓的 Hirota双线性型 .本文对可积方程簇给出此 Hirota双线性型 ,从而该方程簇的孤立子解是可以求出的 .

By Hirota's method, soliton solutions can be directly found from the nonlinear evolution equations . Firstly a dependent variable transformation is introduced in this direct method. The transformation should reduce the evolution equations to a so-called billinear forms. In this paper the bilinear equations of the integrabele equation hierachy are found, so Soliton solutions of the equation hierachy may be obtained.