In this paper we are going to derive two numerical methods for solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method is a nonlinear implicit scheme of second order accuracy in both directions...In this paper we are going to derive two numerical methods for solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method is a nonlinear implicit scheme of second order accuracy in both directions time and space;the scheme is unconditionally stable. The second scheme is a nonlinear implicit scheme of second order accuracy in time and fourth order accuracy in space direction. A generalized method is also derived where the previous schemes can be obtained by some special values of l. The proposed methods will produced a coupled nonlinear tridiagonal system which can be solved by fixed point method. The exact solutions and the conserved quantities for two different tests are used to display the robustness of the proposed schemes.展开更多
The nonlinear interactions of waves with a double-peaked power spectrum have been studied in shallow water. The starting point is the prototypical equation for nonlinear unidirectional waves in shallow water, i.e. the...The nonlinear interactions of waves with a double-peaked power spectrum have been studied in shallow water. The starting point is the prototypical equation for nonlinear unidirectional waves in shallow water, i.e. the Korteweg de Vries equation. By means of a multiple-scale technique two defocusing coupled Nonlinear SchrCMinger equations are derived. It is found analytically that plane wave solutions of such a system are unstable for small perturbations, showing that the existence of a new energy exchange mechanism which can influence the behavior of ocean waves in shallow water.展开更多
文摘In this paper we are going to derive two numerical methods for solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method is a nonlinear implicit scheme of second order accuracy in both directions time and space;the scheme is unconditionally stable. The second scheme is a nonlinear implicit scheme of second order accuracy in time and fourth order accuracy in space direction. A generalized method is also derived where the previous schemes can be obtained by some special values of l. The proposed methods will produced a coupled nonlinear tridiagonal system which can be solved by fixed point method. The exact solutions and the conserved quantities for two different tests are used to display the robustness of the proposed schemes.
基金The paper was financially supporrted by the National Natural Science Foundation of China (Grant No40476062)Foundation of Hebei University of Science and Technology
文摘The nonlinear interactions of waves with a double-peaked power spectrum have been studied in shallow water. The starting point is the prototypical equation for nonlinear unidirectional waves in shallow water, i.e. the Korteweg de Vries equation. By means of a multiple-scale technique two defocusing coupled Nonlinear SchrCMinger equations are derived. It is found analytically that plane wave solutions of such a system are unstable for small perturbations, showing that the existence of a new energy exchange mechanism which can influence the behavior of ocean waves in shallow water.
