On multisymplectic sine collocation discretizations for “Good” Boussinesq equation

摘要

By canonical transformation, multisymplectic systems and multisymplectic conservation laws for nonlinear Good Boussinesq equation with periodic boundary conditions are obtained. Using sine collocation method in spatial direction and Euler centered scheme in time direction to the multisymplectic systems, a multisymplectic sine collocation scheme is constructed. At the same time, we have also obtained semi-discrete and full discrete multisymplectic conservation laws for the scheme. Numerical experiment show that the multisymplectic sine collocation scheme constructed in this paper is effective, and has excellent longtime numerical behavior.