SIAM Journal on Scientific Computing
Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Efficient Numerical Continuation and Stability Analysis of Spatiotemporal Quadratic Optical Solitons
SIAM Journal on Scientific Computing
A mode elimination technique to improve convergence of iteration methods for finding solitary waves
Journal of Computational Physics
A mode elimination technique to improve convergence of iteration methods for finding solitary waves
Journal of Computational Physics
Iteration methods for stability spectra of solitary waves
Journal of Computational Physics
Newton-conjugate-gradient methods for solitary wave computations
Journal of Computational Physics
Simulation of coherent structures in nonlinear Schrödinger-type equations
Journal of Computational Physics
A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave models
Journal of Computational and Applied Mathematics
Solitary Wave Benchmarks in Magma Dynamics
Journal of Scientific Computing
Original article: Lanczos-Chebyshev pseudospectral methods for wave-propagation problems
Mathematics and Computers in Simulation
Hi-index | 31.47 |
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+up=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.