Exact and numerical solutions of the generalized Fisher equation (Q5945643)

The paper deals with the generalized Fisher equation of the form NEWLINE\[NEWLINEU_t= [(\lambda_0 U+\lambda_1) U_x]_x+ \lambda_2, U- \lambda_3 U^2,\tag{1}NEWLINE\]NEWLINE where \(\lambda_0\), \(\lambda_1\), \(\lambda_2\) and \(\lambda_3\in \mathbb{R}\). The authors apply the classical Lie method to find the exact solutions of (1). The analytical results are compared with numerical calculations using the method of finite elements.