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 Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the dispersive shock waves.

On critical behaviour in generalized Kadomtsev-Petviashvili equations / Dubrovin, Boris; Grava, Tamara; Klein, C.. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - 333:October(2016), pp. 157-170. [10.1016/j.physd.2016.01.011]

On critical behaviour in generalized Kadomtsev-Petviashvili equations

Dubrovin, Boris;Grava, Tamara;
2016-01-01

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 Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the dispersive shock waves.
2016
333
October
157
170
Dubrovin, Boris; Grava, Tamara; Klein, C.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11956
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