Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi's Elliptic Function Expansion

被引：4

作者：

Zeng, Xiaohua ^{[1
]}

Wu, Xiling ^{[1
]}

Liang, Changzhou ^{[1
]}

Yuan, Chiping ^{[2
]}

Cai, Jieping ^{[1
]}

机构：

[1] Guangzhou Xinhua Univ, Sch Econ & Trade, Dongguan 523133, Peoples R China

[2] Sun Yat sen Univ, Inst Guangdong, Hong Kong & Macao Dev Studies, Guangzhou 510275, Peoples R China

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 05期

关键词：

coupled KdV equations; variable coefficients; quadratic Jacobi's elliptic function; soliton; traveling wave solution; BACKLUND TRANSFORMATION; WAVE SOLUTIONS;

D O I：

10.3390/sym15051021

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi's elliptic function expansion. The presented coupled KdV equations have a more general form than those studied in the literature. Nine couples of quadratic Jacobi's elliptic function solutions are found. Each couple of traveling wave solutions is symmetric in mathematical form. In the limit cases m ? 1, these periodic solutions degenerate as the corresponding soliton solutions. After the simple parameter substitution, the trigonometric function solutions are also obtained.

引用

页数：10

共 50 条

[1] Abundant exact solutions of higher-order dispersion variable coefficient KdV equation
Zhao, Zhen
Pang, Jing
OPEN PHYSICS, 2022, 20 (01): : 963 - 976
[2] Exact solutions for coupled KdV equation and KdV equations
Inan, Ibrahim E.
PHYSICS LETTERS A, 2007, 371 (1-2) : 90 - 95
[3] Exact solutions for the improved mKdv equation with conformable derivative by using the Jacobi elliptic function expansion method
Farooq, Aamir
Khan, Muhammad Ishfaq
Ma, Wen Xiu
OPTICAL AND QUANTUM ELECTRONICS, 2024, 56 (04)
[4] New Jacobi elliptic functions solutions for the variable-coefficient mKdV equation
Hong, Baojian
APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (08) : 2908 - 2913
[5] New exact solutions for the variable coefficient modified KdV equation using direct reduction method
El-Shiekh, Rehab M.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (01) : 1 - 4
[6] New Exact Jacobi Elliptic Function Solutions for the Coupled Schrodinger-Boussinesq Equations
Hong, Baojian
Lu, Dianchen
JOURNAL OF APPLIED MATHEMATICS, 2013,
[7] EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION
Zhang, Yi
Cheng, Zhilong
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2012, 26 (19):
[8] Exact solutions of the combined KdV-Burgers equation with variable coefficients
Yu, Yaodong
Ma, Hong-Cai
APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (10) : 3534 - 3540
[9] Exact structures for the KdV-mKdV equation with variable coefficients via the functional variable method
Djoudi, W.
Zerarka, A.
OPTIK, 2016, 127 (20): : 9621 - 9626
[10] Optical solitons in birefringent fibers with quadratic-cubic nonlinearity by extended Jacobi's elliptic function expansion
Biswas, Anjan
Ekici, Mehmet
Sonmezoglu, Abdullah
Belic, Milivoj
OPTIK, 2019, 178 : 117 - 121

← 1 2 3 4 5 →