Nonlinear differential equations with exact solutions expressed via the Weierstrass function

被引：19

作者：

Kudryashov, NA ^{[1
]}

机构：

[1] State Univ, Moscow Engn & Phys Inst, Dept Appl Math, Moscow 115409, Russia

来源：

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 2004年 / 59卷 / 7-8期

基金：

俄罗斯基础研究基金会;

关键词：

nonlinear differential equation; exact solution; Weierstrass function; nonlinear evolution equation;

D O I：

10.1515/zna-2004-7-807

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution of the simplest integrable equation. We use the Weierstrass elliptic equation as building block to find a number of nonlinear differential equations with exact solutions. Nonlinear differential equations of the second, third and fourth order with special solutions-expressed via the Weierstrass function are given.

引用

页码：443 / 454

页数：12

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