Explicit Solutions of Some Nonlinear Evolution Equations through Separation of Variables
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.
separation of variablesnonlinear evolution equationexplicit solution
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