Searching for integrable PDE's by testing Hirota's three-soliton condition
Searching for integrable PDE's by testing Hirota's three-soliton condition
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DOI：
10.1145/120694.120739
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发表时间：
1991-06
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影响因子：
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通讯作者：
J. Hietarinta
中科院分区：
文献类型：
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作者：
J. Hietarinta
寻找可积的偏微分方程组一直是一个活跃的研究课题，计算机代数是一个必要的工具。本文根据Hirota的双线性形式中存在标准型三孤子解和四孤子解的要求，描述了一种搜索方法。N-孤子解的存在性可以表示为由M个变量的N个多项式所定义的仿射流形上某个N×A4变量的高次多项式为零的条件。对几类典型方程进行了穷尽搜索，找到了几个新的方程。
The search for integrable PDE’s has been an active research subject with computer algebra as a necessary tool. In this paper we describe a search method based on the requirement that standard type threeand four-soliton solution exist in the bilinear formalism of Hirota. The existence on N-soliton solutions can be formulated as a requirement that a certain high degree polynomial in N x A4 variables vanishes on an affine manifold defined by N polynomials of M vi~riables each. An exhaustive search has been carried out for certain classes of typical equations and several new equations have been found.