New Complex Solutions of the Coupled KdV Equations

FAN Jun-jie , LI Guang-fang , Taogetusang

doi:10.13371/j.cnki.chin.q.j.m.2021.01.003

Chinese Quarterly Journal of Mathematics >

2021 , Vol. 36 >Issue 1: 41 - 48

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.01.003

New Complex Solutions of the Coupled KdV Equations

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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

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.

Received date: 2020-11-22

Online published: 2021-03-30

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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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

Cite this article

FAN Jun-jie , LI Guang-fang , Taogetusang . New Complex Solutions of the Coupled KdV Equations[J]. Chinese Quarterly Journal of Mathematics, 2021 , 36(1) : 41 -48 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.003

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