The method of separation of variables is used to solve some nonlinear evolution equations such as the Harry-Dym equation,the extended Harry-Dym equation,the Hunter-Saxton equation,the nonlinear diffusion equation,the semi-classical limit KdV and mKdV equations and others,by which new explicit solutions of these nonlinear evolution equations are obtained.Interestingly,Bessel functions appear in these solutions.Some of the solutions also give the prediction of blow-up phenomenon.
关键词
分离变量法/非线性发展方程/显式解
Key words
separation of variables/nonlinear evolution equation/explicit solution
维普
万方数据