The Davey-Stewartson equation and the Ablowitz-Ladik hierarchy

被引：9
|
作者：
Vekslerchik, VE
机构：
[1] Inst. Radiophysics and Electronics, Ukrainian Academy of Sciences, Kharkov 310085
来源：
INVERSE PROBLEMS | 1996年 / 12卷 / 06期
关键词：
D O I：
10.1088/0266-5611/12/6/016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A relation between the Davey-Stewartson (DS) system and the Ablowitz-Ladik hierarchy (ALH) is established. It is shown that the former can be 'embedded' into the system of flows described by the ALH. This relation is used to work out a procedure for obtaining a wide range of solutions of the (2 + 1)-dimensional DS equation using the traditional inverse scattering transform that has been developed for (1 + 1)-dimensional systems, without invoking the multidimensional one. The 'embedding into the ALH' method is used to derive the dark soliton, quasiperiodic and some other solutions for the DS-II as well for the Ishimori equation, which is gauge equivalent to the DS system.
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页码：1057 / 1074
页数：18
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