Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 42, Issue 3, Pages 1110-1127Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036142902414232
Keywords
nonlinear evolution equations; solitary waves; numerical approximations; iteration methods; convergence and stability; linearized operators
Categories
Ask authors/readers for more resources
We analyze a heuristic numerical method suggested by V. I. Petviashvili in 1976 for approximation of stationary solutions of nonlinear wave equations. The method is used to construct numerically the solitary wave solutions, such as solitons, lumps, and vortices, in a space of one and higher dimensions. Assuming that the stationary solution exists, we find conditions when the iteration method converges to the stationary solution and when the rate of convergence is the fastest. The theory is illustrated with examples of physical interest such as generalized Korteweg-de Vries, Benjamin-Ono, Zakharov-Kuznetsov, Kadomtsev-Petviashvili, and Klein-Gordon equations.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available