NUMERICAL STUDY OF BLOW-UP IN SOLUTIONS TO GENERALIZED KADOMTSEV-PETVIASHVILI EQUATIONS

被引：11

作者：

Klein, Christian ^{[1
]}

Peter, Ralf ^{[1
]}

机构：

[1] Univ Bourgogne, Inst Math Bourgogne, F-21078 Dijon, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2014年 / 19卷 / 06期

基金：

欧洲研究理事会;

关键词：

Generalized Kadomtsev-Petviasvili equations; blow-up; numerical approaches; dynamic rescaling; KORTEWEG-DE-VRIES; SOLITARY WAVES; CAUCHY-PROBLEM; DECAY;

D O I：

10.3934/dcdsb.2014.19.1689

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we use a dynamic rescaling to identify the type of the singularity. We present the first discussion of the observed blow-up scenarios. We show that the blow-up in solutions to the L-2 critical generalized Kadomtsev-Petviashvili I case is similar to what is known for the L-2 critical generalized Korteweg-de Vries equation. No blow-up is observed for solutions to the generalized Kadomtsev-Petviashvili II equations for n <= 2.

引用

页码：1689 / 1717

页数：29

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