数学季刊 ›› 2021, Vol. 36 ›› Issue (1): 41-48.doi: 10.13371/j.cnki.chin.q.j.m.2021.01.003

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耦合KdV方程组的复合型新解

  

  1. 1. School of Mathematics, Inner Mongolia Honder College of Arts and Sciences, Huhhot 010000,
    China; 2. School of Science, Inner Mongolia Agricultural University, Huhhot 010018, China; 3. School
    of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China
  • 收稿日期:2020-11-22 出版日期:2021-03-30 发布日期:2021-03-30
  • 作者简介:FAN Jun-jie (1987-), male, native of Huhhot, Inner Mongolia, lecturer of Inner Mongolia Honder College of Arts and Sciences, engages in solitary theory and integral system; LI Guang-fang (1989-), female, native of Huhhot, Inner Mongolia, lecturer of Inner Mongolia Normal University, engages in mathematical physical equation; Taogetusang (1964-), male, native of Huhhot, Inner Mongolia, professor of Inner Mongolia Normal University, engages in solitary theory and integral system.
  • 基金资助:
    Supported by the Natural Natural Science Foundation of China (Grant No: 11361040);

    Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No: NJZY16180); 

    Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No: 2015MS0128).


New Complex Solutions of the Coupled KdV Equations

  1. 1. School of Mathematics, Inner Mongolia Honder College of Arts and Sciences, Huhhot 010000,
    China; 2. School of Science, Inner Mongolia Agricultural University, Huhhot 010018, China; 3. School
    of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China
  • Received:2020-11-22 Online:2021-03-30 Published:2021-03-30
  • About author:FAN Jun-jie (1987-), male, native of Huhhot, Inner Mongolia, lecturer of Inner Mongolia Honder College of Arts and Sciences, engages in solitary theory and integral system; LI Guang-fang (1989-), female, native of Huhhot, Inner Mongolia, lecturer of Inner Mongolia Normal University, engages in mathematical physical equation; Taogetusang (1964-), male, native of Huhhot, Inner Mongolia, professor of Inner Mongolia Normal University, engages in solitary theory and integral system.
  • Supported by:
    Supported by the Natural Natural Science Foundation of China (Grant No: 11361040);

    Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No: NJZY16180); 

    Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No: 2015MS0128).

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摘要：  In this paper, new infinite sequence complex solutions of the coupled KdV equations are constructed with the help of function transformation and the second kind of elliptic equation. First of all, according to the function transformation, the coupled KdV equations are changed into the second kind of elliptic equation. Secondly, the new solutions and B¨acklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled KdV equations. These solutions include new infinite sequence complex solutions composed by Jacobi elliptic
function, hyperbolic function and triangular function.

关键词: The coupled KdV equations, Function transformation, The second kind of elliptic equation, Complex solutions

Abstract:  In this paper, new infinite sequence complex solutions of the coupled KdV equations are constructed with the help of function transformation and the second kind of elliptic equation. First of all, according to the function transformation, the coupled KdV equations are changed into the second kind of elliptic equation. Secondly, the new solutions and B¨acklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled KdV equations. These solutions include new infinite sequence complex solutions composed by Jacobi elliptic
function, hyperbolic function and triangular function.

Key words: The coupled KdV equations, Function transformation, The second kind of elliptic equation, Complex solutions

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