Resonant multiple wave solutions to some integrable soliton equations

doi:10.1088/1674-1056/ab4d47

Abstract To transform the exponential traveling wave solutions to bilinear differential equations, a sufficient and necessary condition is proposed. Motivated by the condition, we extend the results to the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation, the (3+1)-dimensional generalized Kadomtsev-Petviashvili (g-KP) equation, and the B-type Kadomtsev-Petviashvili (BKP) equation. Aa a result, we obtain some new resonant multiple wave solutions through the parameterization for wave numbers and frequencies via some linear combinations of exponential traveling waves. Finally, these new resonant type solutions can be displayed in graphs to illustrate the resonant behaviors of multiple wave solutions.

Keywords: linear superposition principle resonant multiple wave solutions (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation (3+1)-dimensional g-KP and BKP equations

Received: 21 August 2019
Revised: 18 September 2019
Accepted manuscript online:

PACS:	02.30.Ik	(Integrable systems)
	02.60.Cb	(Numerical simulation; solution of equations)
	02.70.Wz	(Symbolic computation (computer algebra))

Fund: Project supported by the Yue-Qi Scholar of the China University of Mining and Technology (Grant No. 102504180004) and the 333 Project of Jiangsu Province, China (Grant No. BRA2018320).

Corresponding Authors: Xiao-Jun Yang
E-mail: xjyang@cumt.edu.cn

Cite this article:

Jian-Gen Liu(刘建根), Xiao-Jun Yang(杨小军), Yi-Ying Feng(冯忆颖) Resonant multiple wave solutions to some integrable soliton equations 2019 Chin. Phys. B 28 110202

[1]	Hietarinta J 2005 Phys. AUC 15 31
[2]	Jin M Z and Yao M Z 2011 Chin. Phys. B 20 010205
[3]	Zhang Y F and Ma W X 2015 Appl. Math. Comput. 256 252
[4]	Zhang Y F and Ma W X 2015 Z. Natur. A 70 263
[5]	Ma W X, Huang T and Zhang Y 2010 Phys. Scripta 82 065003
[6]	Ma W X 2015 Phys. Lett. A 379 1975
[7]	Chao Q, Rao J G, Liu Y B and He J S 2016 Chin. Phys. Lett. 33 110201
[8]	Liu J G and Zhang Y F 2018 Z. Natur. A 73 143
[9]	Yang X J and J A T M 2019 Math. Meth. Appl. Sci. (accepted)
[10]	Gao F, Yang X J and Ju Y 2019 Fractals 27 1940010
[11]	Ma W X 2019 Mathematics 7 573
[12]	Lü X, Wang J P, Lin F H and Zhou X W 2018 Nonl. Dyn. 91 1249
[13]	Liu J G and Zhang Y F 2018 Result. Phys. 10 94
[14]	Liu J G, Wu P X, Zhang Y F and Feng B L 2017 Therm. Sci. 21 169
[15]	Ma W X and Zhou Y 2018 J. Diff. Equ. 264 2633
[16]	Ma W X, Li J and Khalique C M 2018 Complexity 2018 9059858
[17]	Ma W X 2019 Front. Math. Chin. 14 619
[18]	Ma W X 2019 J. Appl. Anal. Comput. 9 1319
[19]	Xu S Q and Geng X G 2018 Chin. Phys. B 27 120202
[20]	Zhou Z K, Xia T C and Ma X 2018 Chin. Phys. B 27 070201
[21]	Ömer ünsal and Ma W X 2016 Comput. Math. Appl. 71 1242
[22]	Zhou Y and Ma W X 2017 Comput. Math. Appl. 73 1697
[23]	Ma W X, Zhang Y, Tang Y and Tu J 2012 Appl. Math. Comput. 218 7174
[24]	Zheng H C, Ma W X and Gu X 2008 Appl. Math. Comput. 220 226
[25]	Ma W X and Fan E G 2011 Comput. Math. Appl. 61 950
[26]	Liu J G, Zhang Y F and Muhammad I 2018 Comput. Math. Appl. 75 3939
[27]	Lin F H, Chen S T, Qu Q X, Wang J P, Zhou X W and Lü X 2018 Appl. Math. Lett. 78 112
[28]	Hirota R 1980 Direct Methods in Soliton Theory (Berlin:Springer) p. 157
[29]	Zhang L, Khalique C M and Ma W X 2016 Int. J. Mod. Phys. B 30 1640029
[30]	Ohta Y, Satsuma J, Takahashi D and Tokihiro T 1998 Prog. Theor. Phys. Suppl. 94 210
[31]	Harada H 1985 J. Phys. Soc. Jpn. 54 4507
[32]	Harada H 1987 J. Phys. Soc. Jpn. 56 3847
[33]	Adamu M Y and Suleiman E 2014 Am. J. Comput. Appl. Math. 4 155

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