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arXiv · 0707.1802

On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

S. V. Manakov·P. M. Santini
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Abstract

We make use of the nonlinear Riemann Hilbert problem of the dispersionless Kadomtsev Petviashvili equation, i) to construct the longtime behaviour of the solutions of its Cauchy problem; ii) to characterize a class of implicit solutions; iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.

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S. V. Manakov, P. M. Santini. 2007-11-20. On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking. https://doi.org/10.1088/1751-8113%2F41%2F5%2F055204

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