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arXiv · 1510.01580

On critical behaviour in generalized Kadomtsev--Petviashvili equations

Boris Dubrovin·Tamara Grava·Christian Klein
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Abstract

An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev--Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painleve' I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture.

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Boris Dubrovin, Tamara Grava, Christian Klein. 2015-10-06. On critical behaviour in generalized Kadomtsev--Petviashvili equations. https://doi.org/10.1016/j.physd.2016.01.011

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