Covariant hodograph transformations between nonlocal short pulse models and the AKNS(-1) system

被引：24
作者：
Chen, Kui [1 ]
Liu, Shimin [1 ]
Zhang, Da-jun [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2019年 / 88卷
关键词：
Nonlocal hodograph transformation; AKNS(-1); Short pulse equation; Nonlocal reduction; NONLINEAR-EVOLUTION-EQUATIONS; COMPLEX SHORT-PULSE; HIERARCHY; REDUCTION;
D O I：
10.1016/j.aml.2018.09.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper presents hodograph transformations between nonlocal short pulse models and the first member in the Ablowitz-Kaup-Newell-Segur negative hierarchy (AKNS(-1)). Multi-component cases are also considered. It is shown that the independent variables of the short pulse models and AKNS(-1) that are connected via hodograph transformations are covariant in nonlocal reductions. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码：230 / 236
页数：7
相关论文
共 28 条
  • [1] Integrable Nonlocal Nonlinear Schrodinger Equation
    Ablowitz, Mark J.
    Musslimani, Ziad H.
    [J]. PHYSICAL REVIEW LETTERS, 2013, 110 (06)
  • [2] NONLINEAR-EVOLUTION EQUATIONS OF PHYSICAL SIGNIFICANCE
    ABLOWITZ, MJ
    KAUP, DJ
    NEWELL, AC
    SEGUR, H
    [J]. PHYSICAL REVIEW LETTERS, 1973, 31 (02) : 125 - 127
  • [3] Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy
    Chen, Kui
    Deng, Xiao
    Lou, Senyue
    Zhang, Da-jun
    [J]. STUDIES IN APPLIED MATHEMATICS, 2018, 141 (01) : 113 - 141
  • [4] Notes on Canonical Forms of Integrable Vector Nonlinear Schrodinger Systems
    Chen, Kui
    Zhang, Da-Jun
    [J]. CHINESE PHYSICS LETTERS, 2017, 34 (10)
  • [5] Solutions of the nonlocal nonlinear Schrodinger hierarchy via reduction
    Chen, Kui
    Zhang, Da-jun
    [J]. APPLIED MATHEMATICS LETTERS, 2018, 75 : 82 - 88
  • [6] Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schrodinger equations
    Deng, Xiao
    Lou, Senyue
    Zhang, Da-jun
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2018, 332 : 477 - 483
  • [7] Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation
    Feng, Bao-Feng
    Maruno, Ken-Ichi
    Ohta, Yasuhiro
    [J]. STUDIES IN APPLIED MATHEMATICS, 2017, 138 (03) : 343 - 367
  • [8] Defocusing complex short-pulse equation and its multi-dark-soliton solution
    Feng, Bao-Feng
    Ling, Liming
    Zhu, Zuonong
    [J]. PHYSICAL REVIEW E, 2016, 93 (05)
  • [9] Complex short pulse and coupled complex short pulse equations
    Feng, Bao-Feng
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2015, 297 : 62 - 75
  • [10] EXAMPLE OF SOLITON BEHAVIOR IN A ROTATING BAROCLINIC FLUID
    GIBBON, JD
    JAMES, IN
    MOROZ, IM
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1979, 367 (1729) : 219 - 237
123