局部微分求积法的深水包络孤立波数值模拟

Numerical simulations of deep-water envelope solitons using localized differential quadrature(LDQ) method

利用局部微分求积法(LDQ)对非线性薛定谔(Schr dinger)方程进行数值求解,分别模拟了单深水孤立波运动,同向双深水孤立波追赶碰撞耦合运动,高阶孤立波振动和孤立波的反射与透射现象,得到各情况下的数值结果。从数值模拟及图像中揭示非线性薛定谔方程的性质和特点,阐述深水孤立波形成的物理意义、运动方式和运动规律,分析在不同初值条件下波形的变化特点,验证了LDQ法对该类问题的有效性。

The nonlinear Schrdinger equation describes the evolution of the envelope of modulated wave groups.This equation has soliton solutions.Numerical simulations of Nonlinear Schrdinger Equation are studied using localized differential quadrature method.Propagation of a deep-water soliton and interaction of two deep-water solitons in the same direction,the Higher-order soliton′s vibration and the soliton′s reflection and transmission are simulated.The numerical results of every case are obtained.The properties and characteristics of the nonlinear Schrdinger equation are obtained from numerical simulations and images.The physical meanings,motion modes and motion laws of deep-water solitons are discussed.The waveform changes at different initial conditions are analyzed.The validity of LDQ method for solving this kind of problems is proved.