Classification of the line-soliton solutions of KPII

被引:83
作者
Chakravarty, Sarbarish [1 ]
Kodama, Yuji [2 ]
机构
[1] Univ Colorado, Dept Math, Colorado Springs, CO 80933 USA
[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA
基金
美国国家科学基金会;
关键词
D O I
10.1088/1751-8113/41/27/275209
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| -> infinity. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.
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页数:33
相关论文
共 29 条
[1]  
Ablowitz M.J., 1991, SOLITONS NONLINEAR E
[2]   Soliton solutions of the Kadomtsev-Petviashvili II equation [J].
Biondini, G ;
Chakravarty, S .
JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (03)
[3]   On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy [J].
Biondini, G ;
Kodama, Y .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (42) :10519-10536
[4]   Elastic and inelastic line-soliton solutions of the Kadomtsev-Petviashvili II equation [J].
Biondini, Gino ;
Chakravarty, Sarbarish .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2007, 74 (2-3) :237-250
[5]  
Bona M., 2004, Combinatorics of Permutations, DOI DOI 10.1201/9780203494370
[6]  
CHAKRAVARTY S, 2008, CONTEMP MAT IN PRESS
[7]  
CHAKRAVARTY S, COMBINATORICS UNPUB
[8]   Crossings and alignments of permutations [J].
Corteel, Sylvie .
ADVANCES IN APPLIED MATHEMATICS, 2007, 38 (02) :149-163
[9]   SOLITON-SOLUTIONS OF THE KORTEWEG-DEVRIES AND KADOMTSEV-PETVIASHVILI EQUATIONS - THE WRONSKIAN TECHNIQUE [J].
FREEMAN, NC ;
NIMMO, JJC .
PHYSICS LETTERS A, 1983, 95 (01) :1-3
[10]  
FREEMAN NC, 1980, ADV APPL MECH, V20, P1