On critical behaviour in generalized Kadomtsev-Petviashvili equations

[摘要] 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. 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. (C) 2016 Elsevier B.V. All rights reserved.

[发布日期] 2016-10-15

[效力级别]  Proceedings Paper

[关键词] Kadomtsev-Petviashvili equations;Dispersive shocks;Painleve equations