Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations

被引：47
|
作者：
Yilmaz, Halis [1 ,2 ]
机构：
[1] Univ Glasgow, Sch Math & Stat, Glasgow G12 8QW, Lanark, Scotland
[2] Dicle Univ, Dept Math, TR-21280 Diyarbakir, Turkey
来源：
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2015年 / 22卷 / 01期
关键词：
Gerdjikov-Ivanov equation; Derivative nonlinear Schrodinger equation; Darboux transformation; Quasideterminants; 35C08; 35Q55; 37K10; 37K35; ROGUE WAVES; SOLITON; SYSTEMS;
D O I：
10.1080/14029251.2015.996438
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the Gerdjikov-Ivanov (GI) equation and present a standard Darboux transformation for it. The solution is given in terms of quasideterminants. Further, the parabolic, soliton and breather solutions of the GI equation are given as explicit examples.
引用
收藏
页码：32 / 46
页数：15
相关论文
共 50 条
  • [21] The Darboux Transformation and N-Soliton Solutions of Gerdjikov-Ivanov Equation on a Time-Space Scale
    Dong, Huanhe
    Huang, Xiaoqian
    Zhang, Yong
    Liu, Mingshuo
    Fang, Yong
    AXIOMS, 2021, 10 (04)
  • [22] Some localized wave solutions for the coupled Gerdjikov-Ivanov equation
    Dong, Min-Jie
    Tian, Li-Xin
    Wei, Jing-Dong
    Wang, Yun
    APPLIED MATHEMATICS LETTERS, 2021, 122
  • [23] Exact single travelling wave solutions to the fractional perturbed Gerdjikov-Ivanov equation in nonlinear optics
    Xiao, Xiang
    Yin, Zhixiang
    MODERN PHYSICS LETTERS B, 2021, 35 (22):
  • [24] Bifurcations and Exact Solutions for the Perturbed Gerdjikov-Ivanov Model with Full Nonlinearity
    Liang, Jianli
    Jin, Xianghua
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2025,
  • [25] Optical solitons for perturbed Gerdjikov-Ivanov equation
    Kaur, Lakhveer
    Wazwaz, Abdul-Majid
    OPTIK, 2018, 174 : 447 - 451
  • [26] Bright, dark and kink exact soliton solutions for perturbed Gerdjikov-Ivanov equation with full nonlinearity
    Farahat, S. E.
    EL Shazly, E. S.
    El-Kalla, I. L.
    Kader, A. H. Abdel
    OPTIK, 2023, 277
  • [27] New optical solitons and traveling wave solutions for the Gerdjikov-Ivanov equation
    Khuri, S. A.
    OPTIK, 2022, 268
  • [28] Closed Form Solutions of the Perturbed Gerdjikov-Ivanov Equation With Variable Coefficients
    Gomez, C. A.
    Jhangeer, A.
    Rezazadeh, H.
    Talarposhti, R. A.
    Bekir, A.
    EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2021, 11 (01) : 207 - 218
  • [29] N-Fold generalized Darboux transformation and semirational solutions for the Gerdjikov-Ivanov equation for the Alfven waves in a plasma
    Chen, Su-Su
    Tian, Bo
    Tian, He-Yuan
    Yang, Dan-Yu
    NONLINEAR DYNAMICS, 2022, 108 (02) : 1561 - 1572
  • [30] Two reliable techniques for the soliton solutions of perturbed Gerdjikov-Ivanov equation
    Arshed, Saima
    OPTIK, 2018, 164 : 93 - 99
12345