D'Alembert wave and soliton molecule of the generalized Nizhnik-Novikov-Veselov equation

被引：7
作者：
Ma, Hongcai [1 ,2 ]
Gao, Yidan [1 ]
Deng, Aiping [1 ,2 ]
机构：
[1] Donghua Univ, Dept Appl Math, Shanghai 201620, Peoples R China
[2] Donghua Univ, Inst Nonlinear Sci, Shanghai 201620, Peoples R China
来源：
MODERN PHYSICS LETTERS B | 2021年 / 35卷 / 31期
基金：
中国国家自然科学基金;
关键词：
D'Alembert; Hirota's bilinear method; soliton molecule; velocity resonant mechanism; (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation; VARIABLE SEPARATION SOLUTIONS;
D O I：
10.1142/S0217984921504820
中图分类号：
O59 [应用物理学];
学科分类号：
摘要：
Traveling wave solution is one of the effective methods for solving nonlinear partial differential equations. D'Alembert solution is a special kind of traveling wave solution. There have been many studies about D'Alembert solution. In this paper, we will solve D'Alembert-type wave solutions for (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Based on the Hirota bilinear transformation and velocity resonance mechanism, the states of soliton molecules composed of two solitons, three solitons and four solitons are studied. It is concluded that D'Alembert-type wave is closely related to soliton molecules.
引用
收藏
页数：11
相关论文
共 24 条
  • [1] Lumps and rogue waves of generalized Nizhnik-Novikov-Veselov equation
    Albares, P.
    Estevez, P. G.
    Radha, R.
    Saranya, R.
    [J]. NONLINEAR DYNAMICS, 2017, 90 (04) : 2305 - 2315
  • [2] Exponential polynomials
    Bell, ET
    [J]. ANNALS OF MATHEMATICS, 1934, 35 : 258 - 277
  • [3] ON THE SPECTRAL TRANSFORM OF A KORTEWEG-DEVRIES EQUATION IN 2 SPATIAL DIMENSIONS
    BOITI, M
    LEON, JJP
    MANNA, M
    PEMPINELLI, F
    [J]. INVERSE PROBLEMS, 1986, 2 (03) : 271 - 279
  • [4] Variable separation solutions for the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation
    Dai, Chaoqing
    Zhang, Jiefang
    [J]. CHAOS SOLITONS & FRACTALS, 2007, 33 (02) : 564 - 571
  • [5] Long-Time Asymptotics for the Spin-1 Gross-Pitaevskii Equation
    Geng, Xianguo
    Wang, Kedong
    Chen, Mingming
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2021, 382 (01) : 585 - 611
  • [6] Explicit quasi-periodic solutions of the Kaup-Newell hierarchy
    Geng, Xianguo
    Li, Zhu
    Xue, Bo
    Guan, Liang
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 425 (02) : 1097 - 1112
  • [7] NEW FORM OF BACKLUND TRANSFORMATIONS AND ITS RELATION TO INVERSE SCATTERING PROBLEM
    HIROTA, R
    [J]. PROGRESS OF THEORETICAL PHYSICS, 1974, 52 (05): : 1498 - 1512
  • [8] Binary Bell Polynomials Approach to Generalized Nizhnik-Novikov-Veselov Equation
    Hu Xiao-Rui
    Chen Yong
    [J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2011, 56 (02) : 218 - 222
  • [9] Huang WH, 2004, Z NATURFORSCH A, V59, P250
  • [10] Searching for missing D'alembert waves in nonlinear system: Nizhnik-Novikov-Veselov equation
    Jia, Man
    Lou, S. Y.
    [J]. CHAOS SOLITONS & FRACTALS, 2020, 140
123