论文标题
非局部Whitham方程中的孤子和骑士
Solitons and cavitons in a nonlocal Whitham equation
论文作者
论文摘要
研究了针对非局部Whitham方程的孤子和洞穴（具有奇异性的局部溶液）。在第四个导数前的第四阶方程将流动波的参数降低为可逆的汉密尔顿系统，该系统定义在两层的四维空间上。保留在一张纸上的系统的解决方案表示方程式的平滑解决方案，但是通过分支平面进行过渡的解决方案代表跳跃的解决方案。使用分析和数值方法，我们发现了许多类型的同型（以及周期性的）轨道，均具有单调渐近和振荡的轨道。它们对应于初始方程的孤子和洞穴。大多数这样的解决方案的存在显示系统的非常复杂的动力学。
Solitons and cavitons (localized solutions with singularities) for the nonlocal Whitham equations are studied. The equation of a fourth order with a parameter in front of fourth derivative for traveling waves is reduced to a reversible Hamiltonian system defined on a two-sheeted four-dimensional space. Solutions of the system which stay on one sheet represent smooth solutions of the equation but those which perform transitions through the branching plane represent solutions with jumps. Using analytic and numerical methods we found many types of homoclinic (and periodic as well) orbits to the equilibria both with a monotone asymptotics and oscillating ones. They correspond to solitons and cavitons of the initial equation. The presence of majority such solutions displays the very complicated dynamics of the system.
