Ito型耦合KdV方程的高阶保能量方法

High Order Energy Preserving Method for the Ito-type Coupled KdV Equations

构造具有能量守恒特性的Ito型耦合KdV方程的高阶保能量格式在模拟方程的运动中有重要的意义.本文利用四阶平均向量场方法和拟谱方法得到了Ito型耦合KdV方程的高阶保能量格式,并利用高阶保能量格式数值模拟方程孤立波的演化行为.数值结果表明新的高阶保能量格式能很好地模拟Ito型耦合KdV方程孤立波的行为,且精确地保持了方程的离散能量守恒.

Constructing the high order energy preserving scheme for the Ito-type coupled KdV equation with the energy conservation property has the important application in simulating the motion of the equation. In this paper, the high order energy preserving scheme for the Ito-type coupled KdV equation is obtained by applying the fourth order average vector field method and the Fourier pseudo spectral method. The new high order energy preserving scheme is applied to simulate the solitary wave behaviors of the equation. Numerical results show the new high order energy preserving scheme can well simulate the solitary wave evolution behaviors of the Ito-type coupled KdV equation and preserve the discrete energy conservation exactly.