On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation

被引：17

作者：

Khusnutdinova, K. R. ^{[1
]}

Klein, C. ^{[2
]}

Matveev, V. B. ^{[2
]}

Smirnov, A. O. ^{[3
]}

机构：

[1] Loughborough Univ Technol, Dept Math Sci, Loughborough LE11 3TU, Leics, England

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

[3] St Petersburg Univ Aerosp Instrumentat, St Petersburg 190000, Russia

来源：

CHAOS | 2013年 / 23卷 / 01期

关键词：

HYPERELLIPTIC THETA-FUNCTIONS; SOLITON-SOLUTIONS; EVOLUTION; WAVES;

D O I：

10.1063/1.4792268

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4792268]

引用

页数：13

共 33 条

[1]

Ablowitz M., 1981, SOLITONS INVERSE SCA, DOI [10.1137/1.9781611970883, DOI 10.1137/1.9781611970883]

[2]

Ablowitz M J., 2011, Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons

[3] EVOLUTION OF PACKETS OF WATER-WAVES [J].

ABLOWITZ, MJ ;

SEGUR, H .

JOURNAL OF FLUID MECHANICS, 1979, 92 (JUN) :691-715

[4]

[Anonymous], 1977, RUSSIAN MATH SURVEYS, DOI [DOI 10.1070/RM1977V032N06ABEH003862, 10.1070/RM1977v032n06ABEH003862]

[5]

Belokolos E. D., 1994, Algebro-geometric approach to nonlinear integrable equations

[6] Soliton solutions of the Kadomtsev-Petviashvili II equation [J].

Biondini, G ;

Chakravarty, S .

JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (03)

[7] Line soliton interactions of the Kadomtsev-Petviashvili equation [J].

Biondini, Gino .

PHYSICAL REVIEW LETTERS, 2007, 99 (06)

[8] Soliton Solutions of the KP Equation and Application to Shallow Water Waves [J].

Chakravarty, S. ;

Kodama, Y. .

STUDIES IN APPLIED MATHEMATICS, 2009, 123 (01) :83-151

[9]

DRIUMA VS, 1983, DOKL AKAD NAUK SSSR+, V268, P15

[10] Hyperelliptic theta-functions and spectral methods: KdV and KP solutions [J].

Frauendiener, J. ;

Klein, C. .

LETTERS IN MATHEMATICAL PHYSICS, 2006, 76 (2-3) :249-267

← 1 2 3 4 →