Homoclinic Breathing Wave Solutions and High-Order Rogue Wave Solutions of (3+1)-Dimensional Variable Coefficient Kudryashov-Sinelshchikov Equations

ZHANG Shijie; TAOGETUSANG

doi:10.21656/1000-0887.410387

Volume 42 Issue 8

Aug. 2021

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(8): 852-858

ZHANG Shijie, TAOGETUSANG. Homoclinic Breathing Wave Solutions and High-Order Rogue Wave Solutions of (3+1)-Dimensional Variable Coefficient Kudryashov-Sinelshchikov Equations[J]. Applied Mathematics and Mechanics, 2021, 42(8): 852-858. doi: 10.21656/1000-0887.410387

Citation:

PDF( 1820 KB)

Homoclinic Breathing Wave Solutions and High-Order Rogue Wave Solutions of (3+1)-Dimensional Variable Coefficient Kudryashov-Sinelshchikov Equations

doi: 10.21656/1000-0887.410387

ZHANG Shijie,
TAOGETUSANG^,

Mathematics Science College, Inner Mongolia Normal University, Hohhot 010022, P.R.China

Funds:

The National Natural Science Foundation of China(11361040)

Received Date: 2020-12-17
Rev Recd Date: 2021-01-22

Available Online: 2021-08-14

Abstract

Abstract

Based on the Hirota bilinear method, the homoclinic breathing wave solutions to the (3+1)-dimensional variable coefficient Kudryashov-Sinelshchikov (K-S) equations were obtained by means of the extended homoclinic breathing test method. Homoclinic breathing waves with different structures were given through selection of appropriate values for the parameters of the solution, and the rogue wave solutions to the equation were derived under the limit of the periodicity of the homoclinic breathing wave solutions. Finally, a special high-order polynomial was constructed as a test function to obtain the 1st-order and the 2nd-order rogue wave solutions.

FullText(HTML)

References(17)

References

[2]BAI Yuexing, TEMUERCHAOLU, LI Yan, et al. New types of interaction solutions to the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation[J]. Modern Physics Letters B,2020,34(23): 2050237.

HIROTA R. The Direct Method in Soliton Theory[M]. Cambridge: Cambridge University Press, 2004.

[3]YE Yanlin, HOU Chong, CHENG Dandan, et al. Rogue wave solutions of the vector Lakshmanan-Porsezian-Daniel equation[J]. Physics Letters A,2020,384(11): 126226. DOI: 10.1142/S0217984920502371.

[4]石兰芳, 王明灿, 钱正雅. 应用Riccati-Bernoulli辅助方程求解广义非线性Schrdinger方程和(2+1)维非线性Ginzburg-Landau方程[J]. 应用数学和力学, 2020,41(7): 786-795.(SHI Lanfang, WANG Mingcan, QIAN Zhengya. Solution of generalized nonlinear Schrdinger equations and (2+1)-dimensional nonlinear Ginzburg-Landau equations with a Riccati-Bernoulli auxiliary equation method[J]. Applied Mathematics and Mechanics,2020,41(7): 786-795.(in Chinese))

[5]GAO Ben, ZHANG Yao. Exact solutions and conservation laws of the (3+1)-dimensional B-type Kadomstev-Petviashvili (BKP)-Boussinesq equation[J]. Symmetry,2020,12(1): 97. DOI: 10.3390/sym12010097.

[6]WANG Haifeng, ZHANG Yufeng. Lump, lumpoff and predictable rogue wave solutions of a dimensionally reduced Hirota bilinear equation[J]. Chinese Physics B,2020,29(4): 040501. DOI: 10.1088/1674-1056/ab75d7.

[7]GUO Handong, XIA Tiecheng, HU Beibei. High-order lumps, high-order breathers and hybrid solutions for an extended (3+1)-dimensional Jimbo-Miwa equation in fluid dynamics[J]. Nonlinear Dynamics,2020,100(1): 601-614.

[8]PENG Weiqi, TIAN Shoufu, ZHANG Tiantian. Breather waves and rational solutions in the (3+1)- dimensi- onal Boiti-Leon-Manna-Pempinelli equation[J]. Computers and Mathematics With Applications,2019,77(3): 715-723.

[9]KUDRYASHOV N A, SINELSHCHIKOV D I. Equation for three-dimensional nonlinear waves in liquid with gas bubbles[J]. Physica Scripta,2012,85(2): 25402-25409.

[10]SHAIKHOVA G N, KUTUM B B, ALTAYBAEVA A B, et al. Exact solutions for the (3+1)-dimensional Kudryashov-Sinelshchikov equation[J]. Journal of Physics: Conference Series,2019, 1416: 012030. DOI: 10.1088/1742-6596/1416/1/012030.

[11]TANG Xianglong, CHEN Yong. Lumps, breathers, rogue waves and interaction solutions to a (3+1)-dimensional Kudryashov-Sinelshchikov equation[J]. Modern Physics Letters B,2020,34(12): 2050117. DOI: 10.1142/S0217984920501171.

[12]CHUKKOL Y B, MOHAMAD M N B, MUMINOV M. Explicit solutions to the (3+1)-dimensional Kudryashov-Sinelshchikov equations in bubbly flow dynamics[J]. Journal of Applied Mathematics,2018,2018: 7452786. DOI: 10.1155/2018/7452786.

[13]GAO Xinyi. Density-fluctuation symbolic computation on the (3+1)-dimensional variable-coefficient Kudryashov-Sinelshchikov equation for a bubbly liquid with experimental support[J]. Modern Physics Letters B,2016,30(15): 1650217. DOI: 10.1142/S0217984916502171.

[14]TAN Wei, DAI Zhengde. Spatiotemporal dynamics of lump solution to the (1+1)-dimensional Benjamin-Ono equation[J]. Nonlinear Dynamics,2017,89(4): 2723-2728.

[15]DAI Zhengde, HUANG Jian, JIANG Murong, et al. Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint[J]. Chaos, Solitons & Fractals,2005,26(4): 1189-1194.

[16]CLARKSON P A, ELLEN D. Rational solutions of the Boussinesq equation and applications to rogue waves[J]. Transactions of Mathematics and Its Applications,2017,1(1): 1-26.

[17]HOQUE F, ROSHID H O, ALSHAMMARI F S. Higher-order rogue wave solutions of the Kadomtsev Petviashvili-Benjanim Bona Mahony (KP-BBM) model via the Hirota-bilinear approach[J]. Physica Scripta,2020,95(11): 115215.

Relative Articles

Supplements(0)

Cited By

Proportional views