Resonant solitons of the B-type Kadomtsev-Petviashvili equation. (English) Zbl 1518.35209
Summary: In this letter, we study the resonant soliton interactions for the B-type Kadomtsev-Petviashvili equation. For the interaction between two solitons, we obtain two kinds of resonant interaction in terms of the value of \(A_{ij}\) which determines the interaction intensity. Using the asymptotic analysis, we derive the exact expression of resonant soliton branch. One-resonant three soliton interaction is also discussed. Some graphic analysis are discussed to show these resonant interactions.
Keywords:
B-type Kadomtsev-Petviashvili equation; soliton; resonant soliton interaction; asymptotic analysisReferences:
| [1] | Yang, J., Nonlinear Waves in Integrable and Nonintegrable Systems (2010), SIAM: SIAM Philadelphia · Zbl 1234.35006 |
| [2] | Zhang, H. S.; Wang, L.; Sun, W. R.; Wang, X.; Xu, T., Mechanisms of stationary converted waves and their complexes in the multi-component AB system, Physica D, 419, Article 132849 pp. (2021) · Zbl 1508.35098 |
| [3] | Fang, Y.; Wu, G. Z.; Wang, Y. Y.; Dai, C. Q., Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN, Nonlinear Dyn., 105, 603 (2021) |
| [4] | Yan, Y. Y.; Liu, W. J., Soliton rectangular pulses and bound states in a dissipative system modeled by the variable-coefficients complex cubic-quintic Ginzburg-Landau equation, Chin. Phys. Lett., 38, Article 094201 pp. (2021) |
| [5] | Fang, J. J.; Mou, D. S.; Zhang, H. C.; Wang, Y. Y., Discrete fractional soliton dynamics of the fractional Ablowitz-Ladik model, Optik, 228, Article 166186 pp. (2021) |
| [6] | Wang, R. R.; Wang, Y. Y.; Dai, C. Q., Influence of higher-order nonlinear effects on optical solitons of the complex Swift-Hohenberg model in the mode-locked fiber laser, Opt. Laser Technol., 152, Article 108103 pp. (2022) |
| [7] | Fang, Y.; Wu, G. Z.; Wen, X. K.; Wang, Y. Y.; Dai, C. Q., Predicting certain vector optical solitons via the conservation-law deep-learning method, Opt. Laser Technol., 155, Article 108428 pp. (2022) |
| [8] | Maccari, A., The Kadomtsev-Petviashvili equation as a source of integrable model equations, J. Math. Phys., 37, 6207 (1996) · Zbl 0861.35100 |
| [9] | Rao, J.; He, J.; Malomed, B. A., Resonant collisions between lumps and periodic solitons in the Kadomtsev-Petviashvili I equation, J. Math. Phys., 63, Article 013510 pp. (2022) · Zbl 1507.35226 |
| [10] | Rao, J.; Cheng, Y.; Porsezian, K.; Mihalache, D.; He, J., PT-symmetric nonlocal Davey-Stewartson I equation: soliton solutions with nonzero background, Physica D, 401, Article 132180 pp. (2020) · Zbl 1453.37068 |
| [11] | Zhou, A. J.; Chen, A. H., Exact solutions of the Kudryashov-Sinelshchikov equation in ideal liquid with gas bubbles, Phys. Scr., 93, Article 125201 pp. (2018) |
| [12] | Wu, H. Y.; Jiang, L. H., One-component and two-component Peregrine bump and integrated breather solutions for a partially nonlocal nonlinearity with a parabolic potential, Optik, 262, Article 169250 pp. (2022) |
| [13] | Mulase, M., Complete integrability of the Kadomtsev-Petviashvili equation, Adv. Math., 54, 57 (1984) · Zbl 0587.35083 |
| [14] | Cheng, Y., Modifying the KP, then th constrained KP hierarchies and their Hamiltonian structures, Commun. Math. Phys., 171, 661 (1995) · Zbl 0838.35113 |
| [15] | Lou, S. Y., Symmetries of the Kadomtsev-Petviashvili equation, J. Phys. A, 26, 4387 (1993) · Zbl 0801.35123 |
| [16] | Jimbo, M.; Miwa, T., Solitons and infinite dimensional Lie algebras, Publ. Res. Inst. Math. Sci., 19, 943 (1983) · Zbl 0557.35091 |
| [17] | Hirota, R., Soliton solutions to the BKP equations II: the integral equation, J. Phys. Soc. Jpn., 58, 2705 (1989) |
| [18] | Hirota, R., Soliton solutions to the BKP equations I: the Pfaffian technique, J. Phys. Soc. Jpn., 58, 2285 (1989) |
| [19] | Liang, Y.; Wei, G.; Li, X., Painlevé integrability, similarity reductions, new soliton and soliton-like similarity solutions for the (2+1)-dimensional BKP equation, Nonlinear Dyn., 62, 195 (2010) · Zbl 1208.35018 |
| [20] | Peng, W. Q.; Tian, S. F.; Zhang, T. T., Analysis on lump, lumpoff and rogue waves with predictability to the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation, Phys. Lett. A, 382, 2701 (2018) · Zbl 1404.35396 |
| [21] | Yang, X.; Fan, R.; Li, B., Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation, Phys. Scr., 95, Article 045213 pp. (2020) |
| [22] | Zhang, J.; Ma, W. X., Mixed lump-kink solutions to the BKP equation, Comput. Math. Appl., 74, 591 (2017) · Zbl 1387.35540 |
| [23] | Ma, W. X.; Yong, X.; Lü, X., Soliton solutions to the B-type Kadomtsev-Petviashvili equation under general dispersion relations, Wave Motion, 103, Article 102719 pp. (2021) · Zbl 1524.35508 |
| [24] | Hirota, R., The Direct Method in Soliton Theory (2004), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 1099.35111 |
| [25] | Feng, Y.; Bilige, S., Resonant multi-soliton, M-breather, M-lump and hybrid solutions of a combined pKP-BKP equation, J. Geom. Phys., 169, Article 104322 pp. (2021) · Zbl 1486.35360 |
| [26] | Ohkuma, K.; Wadati, M., The Kadomtsev-Petviashvili equation: the trace method and the soliton resonances, J. Phys. Soc. Jpn., 52, 749 (1983) |
| [27] | Ma, W. X.; Fan, E., Linear superposition principle applying to Hirota bilinear equations, Comput. Math. Appl., 61, 950 (2011) · Zbl 1217.35164 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
