论文标题

截短和弯曲的重力波孤子的演变:马赫膨胀问题

Evolution of truncated and bent gravity wave solitons: the Mach expansion problem

论文作者

Ryskamp, Samuel, Maiden, Michelle D., Biondini, Gino, Hoefer, Mark A.

论文摘要

使用调制理论分析了内部和表面重力波建模的Kadomtsev-PetviaShvili(KPII)方程的最初截短和弯曲线孤子的动力学。与先前关于从急性入射角发展的倾斜相互作用的孤子的研究相反,这项工作集中于两到三个部分孤子的钝化发生率的初始价值问题,这些孔彼此传播。尽管存在反向,但仍有明显的残留孤子相互作用,并带有新的身体后果。截断线孤子描述的截断线的初始值问题是从宽通道中出现的Quasi One维孤子的出现,与斜孤子的相互作用相关。通过与局部孤子振幅和斜率的调制方程相互作用的简单波解解决方案,获得了弱和强相互作用的分析描述。在弱相互作用的情况下,截短和大钝角孤子的长期演变表现出腐烂的抛物线波轮廓,其时间长度增加,从而渐近地增加了圆柱形korteweg-de vries soliton。相比之下,略微钝的孤子相互作用的强相互作用情况会演变成稳定的一维孤子,幅度降低了与入射斜率成正比的量。这种强烈的相互作用与孤子的“马赫膨胀”标识为具有宽阔的角落,与具有压缩角的孤子的众所周知的马赫反射形成对比。有趣的是,马赫膨胀和反射的临界角度是相同的。 KPII方程的数值模拟定量支持分析结果。

The dynamics of initially truncated and bent line solitons for the Kadomtsev-Petviashvili (KPII) equation modelling internal and surface gravity waves are analysed using modulation theory. In contrast to previous studies on obliquely interacting solitons that develop from acute incidence angles, this work focuses on initial value problems for the obtuse incidence of two or three partial line solitons, which propagate away from one another. Despite counterpropagation, significant residual soliton interactions are observed with novel physical consequences. The initial value problem for a truncated line soliton-describing the emergence of a quasi-one-dimensional soliton from a wide channel-is shown to be related to the interaction of oblique solitons. Analytical descriptions for the development of weak and strong interactions are obtained in terms of interacting simple wave solutions of modulation equations for the local soliton amplitude and slope. In the weak interaction case, the long-time evolution of truncated and large obtuse angle solitons exhibits a decaying, parabolic wave profile with temporally increasing focal length that asymptotes to a cylindrical Korteweg-de Vries soliton. In contrast, the strong interaction case of slightly obtuse interacting solitons evolves into a steady, one-dimensional line soliton with amplitude reduced by an amount proportional to the incidence slope. This strong interaction is identified with the "Mach expansion" of a soliton with an expansive corner, contrasting with the well-known Mach reflection of a soliton with a compressive corner. Interestingly, the critical angles for Mach expansion and reflection are the same. Numerical simulations of the KPII equation quantitatively support the analytical findings.

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