论文标题
广义korteweg-de Vries方程的非零背景的行驶波解决方案
Travelling wave solutions on a non-zero background for the generalized Korteweg-de Vries equation
论文作者
论文摘要
对于广义的$ p $ - 功率korteweg-de vries方程，所有具有非零边界条件的非周期性波动波解决方案均针对所有整数功率明确分类为$ p \ geq 1 $。这些解决方案显示出：在奇数$ p $的非零背景上，明亮的孤立波和静态驼峰；在非零背景上的深色孤立波和偶数案例中的$ p $的扭结波；对非零背景上的一对明亮/深色的孤立波，以及在非零背景上的明亮而深色的重尾波（具有功率衰减），甚至在聚焦案例中为$ p $。为每种类型的解决方案术语提供了明确的物理参数化，背景大小$ b $以及波高/深度$ h $。 $（C，B）$以及$（H，B）$中的允许运动区域的存在，并讨论了其他主要运动学特征。明确的公式在可集成的情况下呈现$ p = 1,2 $，在较高功率案例中$ p = 3,4 $。
For the generalized $p$-power Korteweg-de Vries equation, all non-periodic travelling wave solutions with non-zero boundary conditions are explicitly classified for all integer powers $p\geq 1$. These solutions are shown to consist of: bright solitary waves and static humps on a non-zero background for odd $p$; dark solitary waves on a non-zero background and kink waves for even $p$ in the defocusing case; pairs of bright/dark solitary waves on a non-zero background, and also bright and dark heavy-tail waves (with power decay) on a non-zero background, for even $p$ in the focusing case. An explicit physical parameterization is given for each type of solutionin terms of the wave speed $c$, background size $b$, and wave height/depth $h$. The allowed kinematic region in $(c,b)$ as well as in $(h,b)$ for existence of the solutions is derived, and other main kinematic features are discussed. Explicit formulas are presented in the integrable cases $p=1,2$, and in the higher power cases $p=3,4$.
