一类描述伪球面的反应扩散方程及其守恒律  

A kind of reaction-diffusion equation describing pseudo-spherical surface and its conservation laws

作　　者：李倩[1] 邱境亮 黄泽旭 

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《北京信息科技大学学报（自然科学版）》2017年第2期73-77,共5页Journal of Beijing Information Science and Technology University

摘　　要：通过伪球面方法求解耦合非线性反应扩散方程的Lax对及其守恒律。对已知的耦合非线性反应扩散方程,首先引入变量变换,得到该反应扩散方程的微分1-形式,使其满足伪球面条件,并建立相应的方程组,得到满足该微分方程的原始解,进而得到伪球面结构方程的解。然后根据定义,求得Lax对,并对Lax对进行验证,满足零曲率方程。最后,求得反应扩散方程的守恒律。The Lax pair and conservation laws are proposed by means of the approach of pseudo- spherical surface. A proper variable transformation is introduced to get the equivalent differential 1-form of the coupled nonlinear reaction-diffusion equation, which should satisfy the conditions of pseudo- spherical surface. A set of differential equations are derived and their solutions are obtained to satisfy the structure equations of the pseudo-spherical surface. Then the Lax pair of the coupled nonlinear reaction- diffusion equation is obtained by definition, which satisfies the zero-curvature equation. Finally, the conservation laws of the coupled nonlinear reaction-diffusion equation are solved.

关 键 词：伪球面 反应扩散方程 LAX对 零曲率方程 守恒律 

分 类 号：O175.29[理学—数学]