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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 |
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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.
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Received: 17 October 2022
Revised: 26 December 2022
Accepted manuscript online: 13 January 2023
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PACS:
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02.30.Ik
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(Integrable systems)
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05.45.Yv
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(Solitons)
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52.35.Mw
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(Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))
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04.30.Nk
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(Wave propagation and interactions)
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| 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
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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
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[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 |
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