Lamé equation and asymptotic higher-order periodic solutions to nonlinear evolution equations
The perturbation method combined with an auxiliary Lamé equation is proposed to construct asymptotic higher-order periodic solutions to some nonlinear evolution equations. It is shown that the higher-order periodic solutions depend on the eigenfunctions of the Lamé equation; different eigenfunctions corresponds to different higher-order solutions. Since Jacobi elliptic functions are more general than the hyperbolic tangent and secant functions, the results of the paper give corresponding solitary or shock wave solutions. This method is also a computerizing method, which allows to perform complicated and tedious algebraic calculation by means of symbolic computation. The KdV equation, Klein-Gordon equation and Kadomtsev-Petviashvili equation are chosen to illustrate the effectiveness of the suggested method.
asymptotic higher-order periodic solution
scientific article; zbMATH DE number 5569571
scientific article