Title: Convergence of iteration methods for numerical approximation 
of stationary solutions of nonlinear wave equations

Speaker: Dmitry Pelinovsky, McMaster University, Canada

Abstract: We analyze an euristic numerical method suggested by
V.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.