论文标题
圆柱加德纳方程中周期性波的非线性调制
Nonlinear Modulation of Periodic Waves in the Cylindrical Gardner Equation
论文作者
论文摘要
在圆柱加德纳（CG）方程中研究了分散性冲击波（DSW）的传播，这是通过一次（2+1）维度降低到两个空间的相似性来获得的，尺寸dimementional-kadomtsev-petviach-petviaShvili（gardner-kp）方程。我们考虑沿抛物线前沿的阶梯式初始条件。然后，根据适当的Riemann类型变量，CG-WHITHAM调制系统是CG方程中DSW演变的描述。我们的研究得到了数值模拟的支持。比较是在CG方程的直接数值解和从Whitham系统的数值解决方案获得的DSW解决方案之间进行了比较。根据此比较，在解决方案之间发现了一个良好的协议。
The propagation of the dispersive shock waves (DSWs) is investigated in the cylindrical Gardner (cG) equation, which is obtained by employing a similarity reduction to the two space one time (2+1) dimensional Gardner-Kadomtsev-Petviashvili (Gardner-KP) equation. We consider the step-like initial condition along a parabolic front. Then, the cG-Whitham modulation system, which is a description of DSW evolution in the cG equation, in terms of appropriate Riemann type variables is derived. Our study is supported by numerical simulations. The comparison is given between the direct numerical solution of the cG equation and the DSW solution obtained from the numerical solution of the Whitham system. According to this comparison, a good agreement is found between the solutions.
