The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation

doi:10.1088/1674-1056/ad9912

Abstract The $N$-periodic wave solvability problem for the ${\cal N} =1$ supersymmetric Sawada-Kotera-Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the $N$-periodic wave solutions is derived. It has been verified that under certain conditions, the asymptotic relations between $N$-periodic wave solutions and $N$-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.

Keywords: supersymmetry $N$-periodic wave solutions asymptotic relations

Received: 24 October 2024
Revised: 28 November 2024
Accepted manuscript online: 02 December 2024

PACS:	05.45.Yv	(Solitons)
	42.65.Tg	(Optical solitons; nonlinear guided waves)
	03.65.Ge	(Solutions of wave equations: bound states)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12101572 and 12371256), 2024 Shanxi Province Graduate Innovation Project (Grant No. 2024KY615), and the Fundamental Research Program of Shanxi Province of China (Grant No. 202403021211002).

Corresponding Authors: Zhonglong Zhao
E-mail: zhaozlhit@163.com,zhaozl@nuc.edu.cn

Cite this article:

Pengcheng Xin(辛鹏程), Zhonglong Zhao(赵忠龙), and Yu Wang(王宇) The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation 2025 Chin. Phys. B 34 020502

[1] Wess J and Zumino B 1974 Nucl. Phys. B 70 39
[2] Fayet P and Ferrara S 1977 Phys. Rep. 32 249
[3] Mavromatos N E and Sarkar S 2001 New J. Phys. 3 001
[4] Fang P P and Lin J 2024 Phys. Rev. E 109 064219
[5] Siegel W 1979 Nucl. Phys. B 156 135
[6] Alvarez-Gaume L, Becker K, Becker M, Emparan R and Manes J 1993 Int. J. Mod. Phys. A 8 2297
[7] Hassanabadia S, Ghominejad M, Zarrinkamarb S and Hassanabadic H 2013 Chin. Phys. B 22 060303
[8] Tian G H 2012 Chin. Phys. B 21 040301
[9] Grishin V G 1965 Sov. Phys. Usp. 8 379
[10] Tomita K 1966 Proc. Phys. Soc. 88 293
[11] Berezin F A 1987 Introduction to Superanalysis (Dordrecht: Springer Dordrecht) p. 74
[12] Vladimirov V S and Volovich I V 1984 Theor. Math. Phys. 60 743
[13] Riaz H W A and Lin J 2024 Appl. Math. Lett. 158 109217
[14] Gordoa P R and Pickering A 1999 Europhys. Lett. 47 21
[15] Liu X Z and Yu J 2022 Chin. Phys. B 31 050201
[16] Zhao Z L and He L C 2021 Appl. Math. Lett. 122 107497
[17] Meng Y, Fang P P and Lin J 2024 Chin. Phys. Lett. 41 060501
[18] Liu Q P and Manas M 1997 Phys. Lett. B 394 337
[19] Liu Q P and Manas M 2000 Phys. Lett. B 485 293
[20] Shi Q L and Li C Z 2021 J. Geom. Phys. 165 104216
[21] Liu Q P, Popowicz Z and Tian K 2010 J. Math. Phys. 51 093511
[22] Tian K and Liu Q P 2012 Phys. Lett. A 376 2334
[23] Tian K, Liu Q P and Yue W J 2020 J. Math. Phys. 61 043503
[24] Liu Q P 1993 J. Phys. A: Math. Gen. 26 L1239
[25] Bonora L and Sorin A 1997 Phys. Lett. B 407 131
[26] Tu M H and Shaw J C 1999 J. Math. Phys. 40 3021
[27] Carstea A S 2000 Nonlinearity 13 1645
[28] Lü S Q, Hu X B and Liu Q P 2006 J. Phys. Soc. Jpn. 75 064004
[29] Fan E G and Hon Y C 2010 Stud. Appl. Math. 125 343
[30] Fan E G and Hon Y C 2010 Rep. Math. Phys. 66 355
[31] Fan E G 2010 Phys. Lett. A 374 744
[32] Dubrovin B A 1975 Funct. Anal. Appl 9 265
[33] Its A and Matveev V 1975 Funct. Anal. Appl. 9 65
[34] Nakamura A 1979 J. Phys. Soc. Jpn. 47 1701
[35] Nakamura A 1980 J. Phys. Soc. Jpn. 48 1365
[36] Dubrovin B A 1981 Russ. Math. Surv. 36 11
[37] Hirota R 2004 The Direct Method in Soliton Theory (New York: Cambridge University Press) p. 9
[38] Fan E G and Hon Y C 2008 Phys. Rev. E 78 036607
[39] Fan E G 2009 J. Phys. A: Math. Theor. 42 095206
[40] Jin Q N 2000 Inverse Problems 16 1457
[41] Argyros I K and Hilout S 2011 J. Appl. Math. Comput. 35 537
[42] Zhang Y N, Hu X B and Sun J Q 2018 J. Comput. Phys. 355 566
[43] Zhang Y N, Hu X B, He Y and Sun J Q 2019 Commun. Comput. Phys. 26 579
[44] Zhang Y N, Hu X B and Sun J Q 2021 Proc. R. Soc. A 477 20200752
[45] Chen M and Wang Z 2023 Chin. Phys. B 32 090504
[46] Kruglov V I and Houria T 2023 Chin. Phys. Lett. 40 090503
[47] Li Z H and Zhao Z L 2025 Appl. Math. Lett. 160 109313
[48] Xuan Y Y 2008 Commun. Theor. Phys. 49 685
[49] Zhang Y, Cheng Z L and Hao X H 2012 Chin. Phys. B. 21 120203
[50] Farkas H M and Kra I 1992 Riemann Surfaces (New York: Springer- Verlag) p. 9
[51] Fan E G 2010 arXiv:1001.1402v1[nlin.SI]
[52] Yue Y and Zhao Z L 2022 Eur. Phys. J. Plus 137 914
[53] Zhao Z L, Zhang C F, Feng Y X and Yue J 2023 Appl. Math. Lett. 146 108799
[54] Yue J, Zhao Z L and Wazwaz A M 2024 Chin. J. Phys. 89 896
[55] Wang Y, Zhao Z L and Zhang Y F 2024 Europhys. Lett. 146 32002

[1]	Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces Jing-Ying Wei(魏静莹), Qing Wang(王青), and Jian Jing(荆坚). Chin. Phys. B, 2021, 30(11): 110307.
[2]	Linear optical approach to supersymmetric dynamics Yong-Tao Zhan(詹颙涛), Xiao-Ye Xu(许小冶), Qin-Qin Wang(王琴琴), Wei-Wei Pan(潘维韦), Munsif Jan, Fu-Ming Chang(常弗鸣), Kai Sun(孙凯), Jin-Shi Xu(许金时), Yong-Jian Han(韩永建), Chuan-Feng Li(李传锋), Guang-Can Guo(郭光灿). Chin. Phys. B, 2020, 29(1): 014209.
[3]	The nonrelativistic oscillator strength of a hyperbolic-type potential H. Hassanabadi, S. Zarrinkamar, B. H. Yazarloo. Chin. Phys. B, 2013, 22(6): 060202.
[4]	The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics S. Hassanabadi, M. Ghominejad, S. Zarrinkamar, H. Hassanabadi. Chin. Phys. B, 2013, 22(6): 060303.
[5]	Spin and pseudospin symmetries of the Dirac equation with shifted Hulthén potential using supersymmetric quantum mechanics Akpan N. Ikot, Elham Maghsoodi, Eno J. Ibanga, Saber Zarrinkamar, Hassan Hassanabadi. Chin. Phys. B, 2013, 22(12): 120302.
[6]	The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method He Ying (何英), Tao Qiu-Gong (陶求功), Yang Yan-Fang (杨艳芳). Chin. Phys. B, 2012, 21(10): 100303.
[7]	A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study Wang You-Fa(王友法), Lou Sen-Yue(楼森岳), and Qian Xian-Min(钱贤民). Chin. Phys. B, 2010, 19(5): 050202.
[8]	Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential Lu Fa-Lin(陆法林) and Chen Chang-Yuan(陈昌远). Chin. Phys. B, 2010, 19(10): 100309.
[9]	Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials Lu Fa-Lin (陆法林), Chen Chang-Yuan (陈昌远), Sun Dong-Sheng (孙东升). Chin. Phys. B, 2005, 14(3): 463-467.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation

Cite this article:

Online attention