柱面Gardner方程中周期波的非线性调制
Nonlinear Modulation of Periodic Waves in the Cylindrical Gardner Equation
摘要：
本文研究了圆柱形Gardner（cG）方程中的色散激波的传播问题，该方程是通过对二维一维Gardner-Kadomtsev-Petviashvili（Gardner-KP）方程进行相似约化得到的。我们考虑沿抛物面前沿的阶梯状初始条件。然后，cG-Whitham调制系统，这是一个描述DSW演化的cG方程，在适当的黎曼型变量的推导。我们的研究得到了数值模拟的支持。给出了直接数值解的cG方程和DSW解的Whitham系统的数值解之间的比较。根据这种比较，一个很好的协议之间的解决方案。
英文摘要：
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.
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