Artificial boundary method for the Zakharov-Rubenchik equations

The paper aims to study the numerical solution of the Zakharov-Rubenchik equations on unbounded domains, which model the propagation of two kinds of waves in plasma physics, by applying the artificial boundary method. Based on ideas of the operator splitting method and artificial boundary method of hyperbolic system and nonlinear Schrödinger equation, the artificial boundary conditions of the Zakharov-Rubenchik equations are designed on the introduced artificial boundaries to reduce the original problem defined on an unbounded domain into an initial boundary value problem on the bounded computational domain, which can be efficiently solved by finite difference method. A series of auxiliary variables is introduced to rigorously analyze the stability of the reduced initial boundary value problem through energy estimation. Numerical examples are presented to demonstrate the effectiveness of the proposed artificial boundary conditions, validate the theoretical analysis, and simulate the physical phenomena.