On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking
Exactly Solvable and Integrable Systems
2009-11-13 v3
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.
Cite
@article{arxiv.0707.1802,
title = {On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking},
author = {S. V. Manakov and P. M. Santini},
journal= {arXiv preprint arXiv:0707.1802},
year = {2009}
}
Comments
33 pages, 10 figures, few formulas updated