Multidimensional localized solitons

被引:26
作者
Boiti, M [1 ]
Martina, L [1 ]
Pempinelli, F [1 ]
机构
[1] IST NAZL FIS NUCL, I-73100 LECCE, ITALY
关键词
D O I
10.1016/0960-0779(94)E0106-Y
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the main results obtained in the last 5 years thanks to the renewed interest in soliton theory due to this discovery. The theoretical tools needed to understand the unexpected richness of behaviour of multidimensional localized solitons during their mutual scattering are furnished. Analogies and especially discrepancies with the unidimensional case are stressed.
引用
收藏
页码:2377 / 2417
页数:41
相关论文
共 82 条
[51]   MULTIDROMION SOLUTIONS TO THE DAVEY-STEWARTSON EQUATION [J].
HIETARINTA, J ;
HIROTA, R .
PHYSICS LETTERS A, 1990, 145 (05) :237-244
[52]   FERMIONIC ANALYSIS OF DAVEY-STEWARTSON DROMIONS [J].
JAULENT, M ;
MANNA, MA ;
MARTINEZALONSO, L .
PHYSICS LETTERS A, 1990, 151 (6-7) :303-307
[53]   ASYMPTOTIC EXPANSIONS FOR THE TRANSMISSION COEFFICIENTS OF THE SO-CALLED DAVEY-STEWARTSON-I SYSTEM [J].
KAUP, DJ .
INVERSE PROBLEMS, 1993, 9 (03) :417-432
[54]  
Konopelchenko B.G., 1993, SOLITONS MULTIDIMENS
[55]  
Konopelchenko B.G., 1992, INTRO MULTIDIMENSION
[56]  
KONOPELCHENKO BG, 1987, LECTURE NOTES PHYSIC, V270
[57]   HAMILTONIAN-STRUCTURE OF THE DAVEY-STEWARTSON EQUATION AND POISSON BRACKETS OF SCATTERING DATA [J].
KULISH, PP ;
LIPOVSKY, VD .
PHYSICS LETTERS A, 1988, 127 (8-9) :413-417
[58]  
KULISH PP, 1989, J SOVIET MATH, V46, P2083
[59]   NONLINEAR EVOLUTIONS, SPECTRAL TRANSFORM AND SOLITONS IN 3+1 DIMENSIONS [J].
LEON, J .
PHYSICS LETTERS A, 1991, 156 (06) :277-285
[60]   2-DIMENSIONAL SOLITONS OF KADOMTSEV-PETVIASHVILI EQUATION AND THEIR INTERACTION [J].
MANAKOV, SV ;
ZAKHAROV, VE ;
BORDAG, LA ;
ITS, AR ;
MATVEEV, VB .
PHYSICS LETTERS A, 1977, 63 (03) :205-206