Invariant Preserving Schemes for Multi-Symplectic Integrator in Shallow Water Wave Propagation

Abstract

The concept of discrete conservation of symplecticity for discretizations of Partial Differential Equations (PDEs) for shallow water wave is presented. This property is Endemic and we express that it also leads to exact discrete conservation of momentum and energy for propagation of shallow water wave. This restricted property is stronger than the global property which that synthesis over all spatial framework points leads to distinct symplectic scheme in the time route. Multi-symplectic integrators are earned for propagation of shallow water wave and investigate conservation property for multi-symplectic integrator. Numerical simulations are also offered.