Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator

Abstract EN

Combining the compact method with the structure-preserving algorithm, we propose a compact local energy-preserving scheme and a compact local momentum-preserving scheme for the nonlinear Schrödinger equation with wave operator (NSEW).

The convergence rates of both schemes are Oh4+τ2.

The discrete local conservative properties of the presented schemes are derived theoretically.

Numerical experiments are carried out to demonstrate the convergence order and local conservation laws of the developed algorithms.