Hamiltonian Boundary Value Method for the Nonlinear Schrödinger Equation and the Korteweg-de Vries Equation
Year: 2017
Author: Mingzhan Song, Xu Qian, Hong Zhang, Songhe Song
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 4 : pp. 868–886
Abstract
In this paper, we introduce the Hamiltonian boundary value method (HBVM) to solve nonlinear Hamiltonian PDEs. We use the idea of Fourier pseudospectral method in spatial direction, which leads to the finite-dimensional Hamiltonian system. The HBVM, which can preserve the Hamiltonian effectively, is applied in time direction. Then the nonlinear Schrödinger (NLS) equation and the Korteweg-de Vries (KdV) equation are taken as examples to show the validity of the proposed method. Numerical results confirm that the proposed method can simulate the propagation and collision of different solitons well. Meanwhile, the corresponding errors in Hamiltonian and other intrinsic invariants are presented to show the good preservation property of the proposed method during long-time numerical calculation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1356
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 4 : pp. 868–886
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Hamiltonian boundary value method Hamiltonian-preserving nonlinear Schrödinger equation Korteweg-de Vries equation.
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