Modulation theory for soliton resonance and Mach reflection
Modulation theory for soliton resonance and Mach reflection
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DOI：
10.1098/rspa.2021.0823
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Samuel J. Ryskamp;M. Hoefer;G. Biondini
中科院分区：
文献类型：
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作者：
Samuel J. Ryskamp;M. Hoefer;G. Biondini
Kadomtsev-Petviashvili II （KPII）方程的共振y形孤子解被建模为无限调制守恒定律族的激波解。证明了在KPII方程的零色散极限下有效的全二维孤子调制方程可以简化为一维系统。在相同的极限下，从较大的Y孤子干到两个较小的腿的快速转变限制了行进不连续。这种不连续是一维调制方程的满足修正Rankine-Hugoniot跳变条件的多值弱解。这些结果用于解析描述马赫反射问题的动力学，v形初始条件对应于向内斜角入射的孤子。调制理论结果与直接KPII数值模拟结果吻合良好。
Resonant Y-shaped soliton solutions to the Kadomtsev–Petviashvili II (KPII) equation are modelled as shock solutions to an infinite family of modulation conservation laws. The fully two-dimensional soliton modulation equations, valid in the zero dispersion limit of the KPII equation, are demonstrated to reduce to a one-dimensional system. In this same limit, the rapid transition from the larger Y soliton stem to the two smaller legs limits to a travelling discontinuity. This discontinuity is a multivalued, weak solution satisfying modified Rankine–Hugoniot jump conditions for the one-dimensional modulation equations. These results are applied to analytically describe the dynamics of the Mach reflection problem, V-shaped initial conditions that correspond to a soliton incident upon an inward oblique corner. Modulation theory results show excellent agreement with direct KPII numerical simulation.