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

2007/07/31 by S. V. Manakov, P. M. Santini · 1 citation
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1088/1751-8113/41/5/055204

33 pages, 10 figures, few formulas updated

arxiv created 2007/11/20 · arxiv updated 2009/12/01

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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