Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(5): 050205    DOI: 10.1088/1674-1056/acb2c2
GENERAL Prev   Next  

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

Fuzhong Pang(庞福忠), Hasi Gegen(葛根哈斯), and Xuemei Zhao(赵雪梅)
School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China
Abstract  The (2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semi-discrete Kadomtsev-Petviashvili I equation. This paper focuses on investigating the resonant interactions between two breathers, a breather/lump and line solitons as well as lump molecules for the (2+1)-dimensional elliptic Toda equation. Based on the N-soliton solution, we obtain the hybrid solutions consisting of line solitons, breathers and lumps. Through the asymptotic analysis of these hybrid solutions, we derive the phase shifts of the breather, lump and line solitons before and after the interaction between a breather/lump and line solitons. By making the phase shifts infinite, we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons. Through the asymptotic analysis of these resonant solutions, we demonstrate that the resonant interactions exhibit the fusion, fission, time-localized breather and rogue lump phenomena. Utilizing the velocity resonance method, we obtain lump-soliton, lump-breather, lump-soliton-breather and lump-breather-breather molecules. The above works have not been reported in the (2+1)-dimensional discrete nonlinear wave equations.
Keywords:  (2+1)-dimensional elliptic Toda equation      resonant interaction      lump molecules  
Received:  17 October 2022      Revised:  26 December 2022      Accepted manuscript online:  13 January 2023
PACS:  02.30.Ik (Integrable systems)  
  05.45.Yv (Solitons)  
  52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))  
  04.30.Nk (Wave propagation and interactions)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12061051 and 11965014).
Corresponding Authors:  Hasi Gegen     E-mail:  gegen@imu.edu.cn

Cite this article: 

Fuzhong Pang(庞福忠), Hasi Gegen(葛根哈斯), and Xuemei Zhao(赵雪梅) Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation 2023 Chin. Phys. B 32 050205

[1] Schneider T and Stoll E 1980 Phys. Rev. Lett. 45 997
[2] Büttner H and Mertens F G 1979 Solid State Commun. 29 663
[3] Bolterauer H and Opper M 1981 Z. Physik B-Condens. Matter 42 155
[4] Muto V, Scott A C and Christiansen P L 1990 Physica D 44 75
[5] Sakanishi A, Hasegawa M and Ushiyama Y 1996 Phys. Lett. A 221 395
[6] Arnold J M 1998 J. Opt. Soc. Am. A 15 1450
[7] Takasaki K 1996 Commun. Math. Phys. 181 131
[8] Martinec E J 1991 Commun. Math. Phys. 138 437
[9] Gerasimov A, Marshakov A, Mironov A, Morozov A and Orlov A 1991 Nucl. Phys. B 357 565
[10] Toda M 1967 J. Phys. Soc. Jpn. 22 431
[11] Nakamura A 1983 J. Phys. Soc. Jpn. 52 380
[12] Villarroel J and Ablowitz M J 1994 J. Phys. A: Math. Gen. 27 931
[13] Vekslerchik V E 1995 Inverse Probl. 11 463
[14] Narita K 2003 J. Math. Anal. Appl. 281 757
[15] Sun Y L, Ma W X and Yu J P 2020 Math. Methods Appl. Sci. 43 6276
[16] Jia Y C, Lu Y, Yu M and Gegen H S 2021 Adv. Math. Phys. 2021 5211451
[17] Zakharov V E and Shabat A B 1974 Funct. Anal. Appl. 8 226
[18] Satsuma J 1976 J. Phys. Soc. Jpn. 40 286
[19] Tajiri M and Murakami Y 1989 J. Phys. Soc. Jpn. 58 3029
[20] Ablowitz M J and Villarroel J 1997 Phys. Rev. Lett. 78 570
[21] Villarroel J and Ablowitz M J 1999 Commun. Math. Phys. 207 1
[22] Manakov S V, Zakharov V E, Bordag L A, Its A R and Matveev V B 1977 Phys. Lett. A 63 205
[23] Zaitsev A A 1983 Sov. Phys. Dokl. 28 720
[24] Zhang Z, Qi Z Q and Li B 2021 Appl. Math. Lett. 116 107004
[25] Christie D R, Muirhead K J and Hales A L 1978 J. Atmos. Sci. 35 805
[26] Grimshaw R, Pelinovsky E and Talipova T 2007 Surv. Geophys. 28 273
[27] Miles J W 1977 J. Fluid Mech. 79 157
[28] Miles J W 1977 J. Fluid Mech. 79 171
[29] Isojima S, Willox R and Satsuma J 2002 J. Phys. A: Math. Gen. 35 6893
[30] Isojima S, Willox R and Satsuma J 2003 J. Phys. A: Math. Gen. 36 9533
[31] Biondini G and Kodama Y 2003 J. Phys. A: Math. Gen. 36 10519
[32] Lester C, Gelash A, Zakharov D and Zakharov V 2021 Stud. Appl. Math. 147 1425
[33] Johnson R S and Thompson S 1978 Phys. Lett. A 66 279
[34] Sun B N and Wazwaz A M 2018 Nonlinear Dyn. 92 2049
[35] Rao J G, Malomed B A, Cheng Y and He J S 2020 Commun. Nonlinear Sci. 91 105429
[36] Rao J G, Chow K W, Mihalache D and He J S 2021 Stud. Appl. Math. 147 1007
[37] Rao J G, He J S and Malomed B A 2022 J. Math. Phys. 63 013510
[38] Xu Y S, Mihalache D and He J S 2021 Nonlinear Dyn. 106 2431
[39] Stepanyants Y A, Zakharov D V and Zakharov V E 2022 Radiophys. Quantum Electron. 64 665
[40] Jiang L, Li X and Li B 2022 Phys. Scripta 97 115201
[41] Rao J G, Kanna T and He J S 2022 Proc. Roy. Soc. A 478 20210777
[42] Stratmann M, Pagel T and Mitschke F 2005 Phys. Rev. Lett. 95 143902
[43] Rohrmann P, Hause A and Mitschke F 2012 Sci. Rep. 2 866
[44] Rohrmann P, Hause A and Mitschke F 2013 Phys. Rev. A 87 043834
[45] Herink G, Kurtz F, Jalali B, Solli D R and Ropers C 2017 Science 356 50
[46] Krupa K, Nithyanandan K, Andral U, Patrice T D and Grelu P 2017 Phys. Rev. Lett. 118 243901
[47] Ryczkowski P, Närhi M, Billet C, Merolla J M, Genty G and Dudley J M 2018 Nat. Photonics 12 221
[48] Liu X M, Yao X K and Cui Y D 2018 Phys. Rev. Lett. 121 023905
[49] Peng J S and Zeng H P 2019 Commun. Phys. 2 34
[50] Peng J S, Boscolo S, Zhao Z H and Zeng H P 2019 Sci. Adv. 5 eaax1110
[51] Xu G, Gelash A, Chabchoub A, Zakharov V and Kibler B 2019 Phys. Rev. Lett. 122 084101
[52] Möller M, Cheng Y, Khan S D, Zhao B Z, Zhao K, Chini M, Paulus G G and Chang Z H 2012 Phys. Rev. A 86 011401(R)
[53] Dudley J M, Genty G, Mussot A, Chabchoub A and Dias F 2019 Nat. Rev. Phys. 1 675
[54] Lou S Y 2020 J. Phys. Commun. 4 041002
[55] Yang X Y, Zhang Z and Li B 2020 Chin. Phys. B 29 100501
[56] Zhang Z, Guo Q, Li B and Chen J C 2021 Commun. Nonlinear Sci. 101 105866
[57] Zhang Z, Yang X Y and Li B 2020 Nonlinear Dyn. 100 1551
[58] Lou S Y 2020 Chin. Phys. B 29 080502
[59] Xu D H and Lou S Y 2020 Acta Phys. Sin. 69 014208 (in Chinese)
[60] Rao J G, Kanna T, Mihalache D and He J S 2022 Physica D 439 133281
[61] Rao J G, He J S and Cheng Y 2022 Lett. Math. Phys. 112 75
[62] Rao J G, Mihalache D and He J S 2022 Appl. Math. Lett. 134 108362
[63] Yang B and Yang J K 2022 J. Nonlinear Sci. 32 52
[1] Preparation of steady-state entanglement via a laser-excited resonant interaction
Cheng Guang-Ling (程广玲), Chen Ai-Xi (陈爱喜), Geng Jun (耿珺), Zhong Wen-Xue (钟文学), Deng Li (邓黎). Chin. Phys. B, 2012, 21(8): 084206.
[2] Generation of any superposition of coherent states along a straight line via resonant atom-cavity interaction
Zheng Shi-Biao(郑仕标). Chin. Phys. B, 2010, 19(4): 044203.
[3] Decoherence-immune generation of highly entangled states for two atoms
Zheng Shi-Biao(郑仕标). Chin. Phys. B, 2010, 19(4): 044204.
[4] Generation of entanglement molecules via weak coherent field in cavity QED
Su Wan-Jun(苏万钧), Yang Zhen-Biao(杨贞标), and Wu Huai-Zhi(吴怀志). Chin. Phys. B, 2009, 18(2): 593-596.
[5] Generation of four-photon W state via cavity QED
Zhong Zhi-Rong(钟志荣). Chin. Phys. B, 2008, 17(9): 3217-3219.
[6] Generation of entangled coherent states for two cavity modes via resonant interaction with a V-type three-level atom
Zheng Shi-Biao(郑仕标). Chin. Phys. B, 2008, 17(6): 2143-2146.
[7] Generation of various multiatom entangled graph states via resonant interactions
Dong Ping(董萍), Zhang Li-Hua (章礼华), and Cao Zhuo-Liang (曹卓良). Chin. Phys. B, 2008, 17(6): 1979-1984.
[8] Implementation of n-qubit Deutsch--Jozsa algorithm using resonant interaction in cavity QED
Wang Hong-Fu(王洪福) and Zhang Shou(张寿). Chin. Phys. B, 2008, 17(4): 1165-1173.
[9] Scheme for the implementation of 1→3 optimal phase-covariant quantum cloning in ion-trap systems
Yang Rong-Can(杨榕灿), Li Hong-Cai(李洪才), Lin Xiu(林秀), Huang Zhi-Ping(黄志平), and Xie Hong(谢鸿). Chin. Phys. B, 2008, 17(3): 967-970.
[10] Preparation of W state in resonant bimodal cavity quantum electrodynamics
Jia Lian-Jun(贾连军) and Yang Zhen-Biao(杨贞标). Chin. Phys. B, 2007, 16(10): 2980-2983.
[11] Nonclassical properties in the resonant interaction of a three level Λ-type atom with two-mode field in coherent state
Wu Huai-Zhi(吴怀志) and Su Wan-Jun(苏万钧). Chin. Phys. B, 2007, 16(1): 106-110.
[12] Preparation of entangled atomic states through simultaneous nonresonant atom--field interaction
Chen Mei-Feng(陈美锋). Chin. Phys. B, 2006, 15(12): 2847-2849.
[13] Variable separation solutions and new solitary wave structures to the (1+1)-dimensional equations of long-wave-short-wave resonant interaction
Xu Chang-Zhi (徐昌智), He Bao-Gang (何宝钢), Zhang Jie-Fang (张解放). Chin. Phys. B, 2004, 13(11): 1777-1783.
No Suggested Reading articles found!