论文标题
直接建造了一个完整的Whitham孤独的家族
A direct construction of a full family of Whitham solitary waves
论文作者
论文摘要
从较早为重力构建的周期性波开始，我们通过相对波高参数溶液曲线，并使用限制性参数获得完整的单独波浪系列。结果分支从零解决方案开始，在波速速度高度空间中遍历独特的点，并在$φ（0）= \fracμ{2} $时达到一个奇异的最高波。该构建基于统一的估计值，从同一方程的周期性波动的早期工作以及有限的参数和伽利利亚变换中提高了，以排除在负面深度下升级的消失的波浪和波。实际上，可以证明周期波在局部统一地收敛到负尾部的波，然后将其转换为溶液的所需分支。该论文还包含有关签名解决方案的独特性和连续性的一些证据（改善了接触的引理）。
Starting with the periodic waves earlier constructed for the gravity Whitham equation, we parameterise the solution curves through relative wave height, and use a limiting argument to obtain a full family of solitary waves. The resulting branch starts from the zero solution, traverses unique points in the wave speed-wave height space, and reaches a singular highest wave at $φ(0) = \fracμ{2}$. The construction is based on uniform estimates improved from earlier work on periodic waves for the same equation, together with limiting arguments and a Galilean transform to exclude vanishing waves and waves levelling off at negative surface depth. In fact, the periodic waves can be proved to converge locally uniformly to a wave with negative tails, which is then transformed to the desired branch of solutions. The paper also contains some proof concerning uniqueness and continuity for signed solutions (improved touching lemma).
