An extended Petviashvili method for the numerical generation of traveling and localized waves

Abstract

A family of fixed-point iterations is proposed for the numerical computation of traveling waves and localized ground states. The methods are extended versions of Petviashvili type, and they are applicable when the nonlinear term of the system contains homogeneous functions of different degree. The methods are described and applied to several examples of interest, that calibrate their efficiency.

References in corpus (3)

• A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
• A mode elimination technique to improve convergence of iteration methods for finding solitary waves
• Conjugate gradient method for finding fundamental solitary waves

Cited by in corpus (5)

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• Numerical solution of internal-wave systems in the intermediate long wave and the Benjamin-Ono regimes