Rogue wave-type solutions of the mKdV equation and their relation to known NLSE rogue wave solutions

被引：0
|
作者：
A. Ankiewicz
N. Akhmediev
机构：
[1] The Australian National University,Optical Sciences Group, Research School of Physics and Engineering
来源：
Nonlinear Dynamics | 2018年 / 91卷
关键词：
Rogue waves; Modified Korteweg–de Vries; Shallow water; Rational solutions;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present the first four exact rational solutions of the set of rational solutions of the modified Korteweg–de Vries equation. These solutions can be considered as rogue waves of the corresponding equation. Comparison with rogue wave solutions of the nonlinear Schrödinger equation shows a strong analogy between their characteristics, especially for amplitude-to-background ratio. The new solutions may be useful in the theory of rogue waves in shallow water and for light propagation in cubic nonlinear media involving only a few optical cycles.
引用
收藏
页码：1931 / 1938
页数：7
相关论文
共 50 条
  • [11] Homoclinic breather and rogue wave solutions to Maccari equation
    Jiang, Ying
    Xian, Da-Quan
    Kang, Xiao-Rong
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 79 (07) : 1890 - 1894
  • [12] Optical Solitons and Rogue wave solutions of NLSE with variables coefficients and modulation instability analysis
    Aslan, Ebru Cavlak
    Inc, Mustafa
    COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2022, 10 (04): : 905 - 913
  • [13] On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equation
    Dubard, P.
    Gaillard, P.
    Klein, C.
    Matveev, V. B.
    EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2010, 185 (01): : 247 - 258
  • [14] On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equation
    P. Dubard
    P. Gaillard
    C. Klein
    V.B. Matveev
    The European Physical Journal Special Topics, 2010, 185 : 247 - 258
  • [15] Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrodinger equation
    Feng, Lian-Li
    Zhang, Tian-Tian
    APPLIED MATHEMATICS LETTERS, 2018, 78 : 133 - 140
  • [16] Breather and rogue wave solutions of a generalized nonlinear Schrodinger equation
    Wang, L. H.
    Porsezian, K.
    He, J. S.
    PHYSICAL REVIEW E, 2013, 87 (05):
  • [17] Rogue wave solutions to the coupled Sasa-Satsuma equation
    Zhang, Guangxiong
    Chen, Xiyao
    Feng, Bao-Feng
    Wu, Chengfa
    PHYSICA D-NONLINEAR PHENOMENA, 2025, 474
  • [18] Rogue wave solutions of the nonlinear Schrodinger equation with variable coefficients
    Liu, Changfu
    Li, Yan Yan
    Gao, Meiping
    Wang, Zeping
    Dai, Zhengde
    Wang, Chuanjian
    PRAMANA-JOURNAL OF PHYSICS, 2015, 85 (06): : 1063 - 1072
  • [19] General rogue wave solutions to the Sasa-Satsuma equation
    Wu, Chengfa
    Zhang, Guangxiong
    Shi, Changyan
    Feng, Bao-Feng
    IMA JOURNAL OF APPLIED MATHEMATICS, 2025,
  • [20] Rational solitary wave and rogue wave solutions in coupled defocusing Hirota equation
    Huang, Xin
    PHYSICS LETTERS A, 2016, 380 (25-26) : 2136 - 2141
12345