论文标题
延长的浅水波方程
Extended shallow water wave equations
论文作者
论文摘要
使用Euler（或水浪）方程的渐近扩展方法得出了扩展的浅水波方程。这些扩展模型是有效的一个阶，超出了通常的弱非线性，长波近似，并结合了所有适当的色散和非线性项。 Specifically, first we derive the extended Korteweg-de Vries (KdV) equation, and then proceed with the extended Benjamin-Bona-Mahony and the extended Camassa-Holm equations in (1+1)-dimensions, the extended cylindrical KdV equation in the quasi-one dimensional setting, as well as the extended Kadomtsev-Petviashvili and its cylindrical对应（2+1） - 维度。我们以扩展的绿色纳格方程式结束。
Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations. These extended models are valid one order beyond the usual weakly nonlinear, long wave approximation, incorporating all appropriate dispersive and nonlinear terms. Specifically, first we derive the extended Korteweg-de Vries (KdV) equation, and then proceed with the extended Benjamin-Bona-Mahony and the extended Camassa-Holm equations in (1+1)-dimensions, the extended cylindrical KdV equation in the quasi-one dimensional setting, as well as the extended Kadomtsev-Petviashvili and its cylindrical counterpart in (2+1)-dimensions. We conclude with the case of the extended Green-Naghdi equations.
