A Chebyshev pseudospectral multidomain method for the soliton solution of coupled nonlinear Schrdinger equations
The collision of solitary waves is an important problem in both physics and applied mathematics. In this paper, we study the solution of coupled nonlinear Schrdinger equations based on pseudospectral collocation method with domain decomposition algorithm for approximating the spatial variable. The problem is converted to a system of nonlinear ordinary differential equations which will be integrated in time by explicit RungeKutta method of order four. The multidomain scheme has much better stability properties than the single domain. Thus this permits using much larger step size for the time integration which fulfills stability restrictions. The proposed scheme reduces the effects of round-of-error for the Chebyshev collocation and also uses less memory without sacrificing the accuracy. The numerical experiments are presented which show the multidomain pseudospectral method has excellent long-time numerical behavior and preserves energy conservation property.
explicit rungekutta method of order four pseudospectral method coupled nonlinear schrdinger equations (cnls) spectral element method