变系数反应扩散方程的Riccati-Ermakov方程组和显式解
Riccati-Ermakov systems and explicit solutions for variable coefficient reaction-diffusion equations
摘要：
提出了几类变系数非线性反应扩散方程，包括Fisher-KPP型方程和Burgers型方程。特殊的精确解，如行波，合理的，三角波和N波型的解决方案。通过相似变换，变系数满足Riccati或Ermakov方程组。当使用Riccati系统时，建立了有限时间奇点可能发生的条件。所提出的解决方案包含多个参数，提供对解决方案的动态的控制。在补充材料中，我们提供了一个计算机代数验证的解决方案和非平凡动力学的解决方案。
英文摘要：
We present several families of nonlinear reaction diffusion equations with variable coefficients including Fisher-KPP and Burgers type equations. Special exact solutions such as traveling wave, rational, triangular wave and N-wave type solutions are shown. By means of similarity transformations the variable coefficients are conditioned to satisfy Riccati or Ermakov systems of equations. When the Riccati system is used, conditions are established so that finite-time singularities might occur. The solutions presented contain multi-parameters providing a control on the dynamics of the solutions. In the suplementary material, we provide a computer algebra verification of the solutions and exemplify nontrivial dynamics of the solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
