HIROTA DIFFERENCE EQUATION: INVERSE SCATTERING TRANSFORM, DARBOUX TRANSFORMATION, AND SOLITONS

被引：7
|
作者：
Pogrebkov, A. K. [1 ,2 ]
机构：
[1] RAS Moscow, VA Steklov Math Inst, Moscow, Russia
[2] Natl Res Univ Higher Sch Econ, Moscow, Russia
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2014年 / 181卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
Hirota difference equation; inverse scattering transform; soliton; Darboux transformation; EXTENDED RESOLVENT; TODA EQUATION; KPI;
D O I：
10.1007/s11232-014-0237-z
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider the direct and inverse problems for the Hirota difference equation. We introduce the Jost solutions and scattering data and describe their properties. In a special case, we show that the Darboux transformation allows finding the evolution in discrete time and obtaining a recursive procedure for sequentially constructing the Jost solution at an arbitrary time for a given initial value. We consider some properties of the soliton solutions.
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页码：1585 / 1598
页数：14
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