New conservative schemes for Zakharov equation

Abstract

New first order and second order energy preserving schemes are proposed for the Zakharov system. The methods are fully implicit and semi-explicit. It has been found that the first order method is also mass conserving. Concrete schemes have been applied to simulate the soliton evolution of the Zakharov system. Numerical results show that the proposed methods capture the remarkable features of the Zakharov equation. We obtained that the semi-explicit methods are more efficient than the fully implicit methods. Numerical results also show that the new energy preserving schemes well simulate the soliton evolution of the Zakharov system.