KdV hierarchy with time-dependent coefficients: Lax integrability, bilinear Backlund transformation and soliton solutions

被引：3
|
作者：
Zhang, Sheng [1 ]
Zhu, Ran [1 ]
机构：
[1] Bohai Univ, Sch Math & Phys, Jinzhou 121013, Peoples R China
来源：
OPTIK | 2017年 / 142卷
关键词：
KdV hierarchy with time-dependent coefficients; Lax integrability; Bilinear BT; Soliton solution; HAMILTONIAN-STRUCTURE; EQUATION; COUPLINGS;
D O I：
10.1016/j.ijleo.2017.06.018
中图分类号：
O43 [光学];
学科分类号：
070207 ; 0803 ;
摘要：
Starting from the linear problems, we first derive a new Lax integrable Korteweg-de Vries (KdV) hierarchy with time-dependent coefficients. Then a bilinear Backlund transformation (BT) of the variable-coefficient KdV (vcKdV) equation contained in the KdV hierarchy is given. Based on the given bilinear BT, one-soliton solution, two-soliton solution and three-soliton solution are obtained. From these obtained soliton solutions, a uniform formula of explicit n-soliton solutions of the vcKdV equation is summarized. It is graphically shown that the dynamical evolutions of such soliton solutions with time-dependent functions of the KdV hierarchy possess time-varying speeds in the process of propagations. (C) 2017 Elsevier GmbH. All rights reserved.
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页码：463 / 469
页数：7
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