Classification of coupled systems with two-component nonlinear diffusion equations by the invariant subspace method

作者：Changzheng Qu, Chunrong Zhu · 发表于：Journal of Physics A Mathematical and Theoretical · 年份：2009 · DOI：10.1088/1751-8113/42/47/475201 · 被引用次数：51 · 研究领域：Mathematical and Theoretical Epidemiology and Ecology Models、Differential Equations and Numerical Methods、Mathematical Biology Tumor Growth

The invariant subspace method is developed to perform classification of systems with two-component nonlinear diffusion equations, which was carried out with respect to the invariant subspaces defined by linear ordinary differential equations. As a result, the corresponding exact solutions generated by invariant subspaces to the resulting systems are obtained. In most cases, two components of these exact solutions belong to different 'scalar' subspaces. Behaviour to several exact solutions of the systems is described.