A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity

JOURNAL OF COMPUTATIONAL PHYSICS

卷:226

Article

Lakoba, T. I. ; Yang, J.

关键词: petviashvili method;    Nonlinear evolution equations;    solitary waves;    iteration methods;   

DOI  :  10.1016/j.jcp.2007.06.009

来源: Elsevier

【 摘 要 】

The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: -Mu + u(p) = 0, where M is a positive definite self-adjoint operator and p = const. In this paper, we propose a systematic generalization of this method to both scalar and vector Hamiltonian equations with arbitrary form of nonlinearity and potential functions. For scalar equations, our generalized method requires only slightly more computational effort than the original Petviashvili method. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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