Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation

doi:10.1088/1674-1056/acae7d

Abstract We gave the localized solutions, the interaction solutions and the mixed solutions to a reduced (3+1)-dimensional nonlinear evolution equation. These solutions were characterized by superposition formulas of positive quadratic functions, the exponential and hyperbolic functions. According to the known lump solution in the outset, we obtained the superposition formulas of positive quadratic functions by plausible reasoning. Next, we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory. These two kinds of solutions contained superposition formulas of positive quadratic functions, which were turned into general ternary quadratic functions, the coefficients of which were all rational operation of vector inner product. Then we obtained linear superposition formulas of exponential and hyperbolic function solutions. Finally, for aforementioned various solutions, their dynamic properties were showed by choosing specific values for parameters. From concrete plots, we observed wave characteristics of three kinds of solutions. Especially, we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

Keywords: localized solutions mixed solutions Hirota bilinear method linear superposition formulas

Received: 20 October 2022
Revised: 03 December 2022
Accepted manuscript online: 27 December 2022

PACS:	02.30.Ik	(Integrable systems)
	02.30.Jr	(Partial differential equations)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12061054) and Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region of China (Grant No. NJYT-20-A06).

Corresponding Authors: Bilige Sudao
E-mail: inmathematica@126.com

Cite this article:

Hangbing Shao(邵杭兵) and Bilige Sudao(苏道毕力格) Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation 2023 Chin. Phys. B 32 050204

[1] Solli D R, Ropers C, Koonath P and Jalali B 2014 Nature 450 1054
[2] Stenflo L and Marklund M 2009 J. Plasma Phys. 76 293
[3] Benetazzo A, Ardhuin F, Bergamasco F, Guimarães P V, Schwendeman M, Sclavo M, Thomson J and Torselo A 2017 Nature 7 8276
[4] Liu B, Zhang X E, Wang B and Lü X 2022 Mod. Phys. Lett. B 36 2250057
[5] Imai K and Nozaki K 1996 Prog. Theor. Phys. 96 521
[6] Pan C C, Baronio F and Chen S H 2020 Acta Phys. Sin. 69 010504 (in Chinese)
[7] Song C Q and Zhu Z N 2020 Acta Phys. Sin. 69 010204 (in Chinese)
[8] Wazwaz A M 2008 Appl. Math. Comput. 201 489
[9] Hu H C and Liu F Y 2020 Chin. Phys. B 29 40201
[10] Abdel Rady A S, Osman E S and Khalfallah M 2010 Appl. Math. Comput. 217 1385
[11] Wazwaz A M 2007 Appl. Math. Comput. 190 633
[12] Fu W, Zhang D J and Zhou R G 2009 Chin. Phys. Lett. 31 090202
[13] Chen J C, Zheng Y M and Hu Y H 2017 Chin. Phys. Lett. 34 010201
[14] Liu P, Xu H R and Yang J R 2020 Acta Phys. Sin. 69 010203 (in Chinese)
[15] Zhao Y W, Xia J W and Xing Lü 2022 Nonlinear Dyn. 108 4195
[16] Yang X Y, Zhang Z and Li B 2009 Chin. Phys. B 29 100501
[17] Geng X G 2003 J. Phys. A: Math. Gen. 36 2289
[18] Geng X G and Ma Y L 2007 Phys. Lett. A 369 285
[19] Huang L L and Chen Y 2019 Commun. Nonlinear Sci. Numer. Simul. 67 237
[20] Xu D H and Lou S Y 2020 Acta Phys. Sin. 69 014208 (in Chinese)
[21] Li M, Wang B T, Xu T and Shui J J 2020 Acta Phys. Sin. 69 010502 (in Chinese)
[22] Zhang Y and Zhou R G 2017 Chin. Phys. Lett. 31 110203
[23] Chen K and Zhang D J 2016 Chin. Phys. Lett. 33 100201
[24] Wen X Y and Wang H T 2020 Acta Phys. Sin. 69 010205 (in Chinese)
[25] Zhang H Q and Ma W X 2017 Comput. Math. Appl. 73 2339
[26] Tang Y N and Liang Z J 2022 Part. Differ. Equ. Appl. Math. 5 110326
[27] Lü J Q, Bilige S and Chaolu T 2018 Nonlinear Dyn. 91 1669
[28] Raza S T R, Bibi I, Younis M and Bekir A 2021 Chin. Phys. B 30 010502
[29] Liu Y K and Li B 2017 Chin. Phys. Lett. 34 10202
[30] Tang Y N, Tao S Q, Zhou M L and Guan Q 2017 Nonlinear Dyn. 89 429
[31] Pu J C and Hu H C 2018 Appl. Math. Lett. 85 77
[32] Fang T, Wang H, Wang Y H and Ma W X 2019 Commun. Theor. Phys. 71 927
[33] Liu Y K and Li B 2017 Chin. Phys. Lett. 34 10202
[34] Lou S Y 2020 Chin. Phys. B 29 80502
[35] Huang L L, Yue Y F and Chen Y 2018 Comput. Math. Appl. 76 831
[36] Wang H F and Zhang Y F 2020 Chin. Phys. B 29 40501
[37] Qian C, Rao J G, Liu Y B and He J S 2016 Chin. Phys. Lett. 33 110201
[38] Zhang R F and Sudao B 2019 Nonlinear Dyn. 95 3041
[39] Shi Y B and Zhang Y 2017 Commun. Nonlinear Sci. Numer. Simul. 44 120
[40] Issasfa A and Lin J 2020 Commun. Theor. Phys. 72 125003
[41] Lou S Y 2020 Acta Phys. Sin. 69 010503 (in Chinese)
[42] Tang X Y, Cui C J, Liang Z F and Ding W 2021 Nonlinear Dyn. 105 2549
[43] Yin Y H, Lü X and Ma W X 2022 Nonlinear Dyn. 108 4181
[44] Yue Y F, Huang L L and Chen Y 2019 Appl. Math. Lett. 89 70
[45] Chen M D, Li X, Wang Y and Li B 2017 Commun. Theor. Phys. 67 595
[46] Zheng P F and Jia M 2018 Chin. Phys. B 27 120201
[47] Liu J G 2018 Appl. Math. Lett. 86 36
[48] Zhang L L, Yu J P, Ma W X, Khalique C M and Sun Y L 2021 Nonlinear Dyn. 104 4317
[49] Lü X and Chen S J 2021 Nonlinear Dyn. 103 947
[50] Lü X and Chen S J 2021 Commun. Nonlinear Sci. Numer. Simul. 103 105939
[51] Hao X Z and Lou S Y 2022 Math. Method Appl. Sci. 45 5774

[1]	Interaction solutions for the second extended (3+1)-dimensional Jimbo—Miwa equation Hongcai Ma(马红彩), Xue Mao(毛雪), and Aiping Deng(邓爱平). Chin. Phys. B, 2023, 32(6): 060201.
[2]	Propagation and modulational instability of Rossby waves in stratified fluids Xiao-Qian Yang(杨晓倩), En-Gui Fan(范恩贵), and Ning Zhang(张宁). Chin. Phys. B, 2022, 31(7): 070202.
[3]	Solutions of novel soliton molecules and their interactions of (2 + 1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation Hong-Cai Ma(马红彩), Yi-Dan Gao(高一丹), and Ai-Ping Deng(邓爱平). Chin. Phys. B, 2022, 31(7): 070201.
[4]	General M-lumps, T-breathers, and hybrid solutions to (2+1)-dimensional generalized KDKK equation Peisen Yuan(袁培森), Jiaxin Qi(齐家馨), Ziliang Li(李子良), and Hongli An(安红利). Chin. Phys. B, 2021, 30(4): 040503.
[5]	Interaction properties of solitons for a couple of nonlinear evolution equations Syed Tahir Raza Rizvi, Ishrat Bibi, Muhammad Younis, and Ahmet Bekir. Chin. Phys. B, 2021, 30(1): 010502.
[6]	High-order rational solutions and resonance solutions for a (3+1)-dimensional Kudryashov-Sinelshchikov equation Yun-Fei Yue(岳云飞), Jin Lin(林机), and Yong Chen(陈勇). Chin. Phys. B, 2021, 30(1): 010202.
[7]	Stable soliton propagation in a coupled (2+1) dimensional Ginzburg-Landau system Li-Li Wang(王丽丽), Wen-Jun Liu(刘文军). Chin. Phys. B, 2020, 29(7): 070502.
[8]	Localized characteristics of lump and interaction solutions to two extended Jimbo-Miwa equations Yu-Hang Yin(尹宇航), Si-Jia Chen(陈思佳), and Xing Lü(吕兴). Chin. Phys. B, 2020, 29(12): 120502.
[9]	Exact solutions of a (2+1)-dimensional extended shallow water wave equation Feng Yuan(袁丰), Jing-Song He(贺劲松), Yi Cheng(程艺). Chin. Phys. B, 2019, 28(10): 100202.
[10]	Superposition solitons in two-component Bose-Einstein condensates Wang Xiao-Min (王晓敏), Li Qiu-Yan (李秋艳), Li Zai-Dong (李再东). Chin. Phys. B, 2013, 22(5): 050311.
[11]	Periodic-soliton solutions of the (2+1)-dimensional Kadomtsev--Petviashvili equation Zhaqilao(扎其劳) and Li Zhi-Bin(李志斌). Chin. Phys. B, 2008, 17(7): 2333-2338.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation

Cite this article:

Online attention