Abstract
Resonant phenomena have been observed and investigated in various situations, such as plasma experiments, the maritime security and the microtubule in cell physiology. In this paper, abundant resonant behaviors are studied for the (3+1)-dimensional BKP-Boussinesq equation. We mainly discuss the resonant two- and three-soliton solutions in the (x, y)-plane and (x, z)-plane. The characteristics are given for the kink soliton waves, including expressions, maximums, minimums and velocities. The kink soliton waves in the (x, y)-plane are parallel, and the fusion or fission may occur. The kink soliton waves in the (x, z)-plane are not parallel and the resonant phenomena among them are more complicated.
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Chen S.J., Lü X., Novel evolutionary behaviors of the mixed solutions to a generalized Burgers equation with variable coefficients. Commun. Nonlinear Sci. Numer. Simul., 2021, 95: 105628
Chen S.J., Lü X., Lump and lump-multi-kink solutions in the (3+1)-dimensions. Commun. Nonlinear Sci. Numer. Simul., 2022, 109: 106103
Chen S.J., Lü X., Li M.G., Wang F., Derivation and simulation of the M-lump solutions to two (2+1)-dimensional nonlinear equations. Phys. Scr., 2021, 96(9): 095201
Chen S.J., Lü X., Ma W.X., Bäcklund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota–Satsuma–Ito-like equation. Commun. Nonlinear Sci. Numer. Simul., 2020, 83: 105135
Chen S.J., Yin Y.H., Lü X., Elastic collision between one lump wave and multiple stripe waves of nonlinear evolution equations. Commun. Nonlinear Sci. Numer. Simul., 2023, 112: 107205
Gao B., Zhang Y., Exact solutions and conservation laws of the (3+1)-dimensional B-Type Kadomstev–Petviashvili(BKP)–Boussinesq Equation. Symmetry, 2020, 12(1): 97
Hirota R., The Direct Method in Soliton Theory. Cambridge: Cambridge University Press, 2004
Hirota R., Ito M., Resonance of solitons in one dimension. J. Phys. Soc. Japan, 1983, 52(3): 744–748
Hu H., Lu Y., Lie group analysis and invariant solutions of (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Modern Phys. Lett. B, 2020, 34(11): 2050106
Kaur L., Wazwaz A.M., Painlevé analysis and invariant solutions of generalized fifth-order nonlinear integrable equation. Nonlinear Dynam., 2018, 94: 2469–2477
Kaur L., Wazwaz A.M., Bright-dark lump wave solutions for a new form of the (3+1)-dimensional BKP-Boussinesq equation. Rom. Rep. Phys., 2019, 71(1): 102
Liu B., Zhang X.E., Wang B., Lü X., Rogue waves based on the coupled nonlinear Schröodinger option pricing model with external potential. Modern Phys. Lett. B, 2022, 36(15): 2250057
Liu W.H., Zhang Y.F., Dynamics of localized waves and interaction solutions for the (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Adv. Difference Equ., 2020, 2020: 93
Lü X., Chen S.J., Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types. Nonlinear Dynam., 2021, 103: 947–977
Lü X., Chen S.J., New general interaction solutions to the KPI equation via an optional decoupling condition approach. Commun. Nonlinear Sci. Numer. Simul., 2021, 103: 105939
Lü X., Hua Y.F., Chen S.J., Tang X.F., Integrability characteristics of a novel (2+1)-dimensional nonlinear model: Painlevé analysis, soliton solutions, Bäcklund transformation, Lax pair and infinitely many conservation laws. Commun. Nonlinear Sci. Numer. Simul., 2021, 95: 105612
Lü X., Hui H.W., Liu F.F., Bai Y.L., Stability and optimal control strategies for a novel epidemic model of COVID-19. Nonlinear Dynam., 2021, 106: 1491–1507
Ma W.X., N-soliton solutions and the Hirota conditions in (2+1)-dimensions. Opt. Quant. Electron., 2020, 52: 511
Ma W.X., N-soliton solution of a combined pKP-BKP equation. J. Geom. Phys., 2021, 165: 104191
Ma W.X., N-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation. Math. Comput. Simulation, 2021, 190: 270–279
Ma W.X., N-soliton solutions and the Hirota conditions in (1+1)-dimensions. Int. J. Nonlinear Sci. Numer. Simul., 2022, 23(1): 123–133
Ma W.X., Fan E.G., Linear superposition principle applying to Hirota bilinear equations. Comput. Math. Appl., 2011, 61(4): 950–959
Ma W.X., Yong X.L., Lü X., Soliton solutions to the B-type Kadomtsev–Petviashvili equation under general dispersion relations. Wave Motion, 2021, 103: 102719
Ma W.X., Zhang Y., Tang Y.N., Tu J.Y., Hirota bilinear equations with linear subspaces of solutions. Appl. Math. Comput., 2012, 218(13): 7174–7183
Nikitenkova S.P., Kovriguine D.A., Stationary multi-wave resonant ensembles in a micro-tubule. Commun. Nonlinear Sci. Numer. Simul., 2019, 67: 314–333
Rahmonov I.R., Tekic J., Mali P., Irie A., Plecenik A., Shukrinov Y.M., Resonance phenomena in an annular array of underdamped Josephson junctions. Phys. Rev. B, 2020, 101(17): 174515
Soomere T., Jüri E., Weakly two-dimensional interaction of solitons in shallow water. Eur. J. Mech. B Fluids, 2006, 25(5): 636–648
Sreekumar J., Nandakumaran V.M., Soliton resonances in helium films. Phys. Lett. A, 1985, 112(3–4): 168–170
Verma P., Kaur L., Analytic study of (3+1)-dimensional Kadomstev–Petviashvili–Boussinesq equation: Painlevé analysis and exact solutions. In: Proceedings of the International Conference on Frontiers in Industrial and Applied Mathematics, 1975, Melville, NY: AIP Publishing, 2018, 030022
Verma P., Kaur L., Integrability, bilinearization and analytic study of new form of (3+1)-dimensional B-type Kadomstev–Petviashvili (BKP)-Boussinesq equation. Appl. Math. Comput., 2019, 346: 879–886
Verma P., Kaur L., Solitary Wave Solutions for (1+2)-dimensional nonlinear Schrödinger equation with dual power law nonlinearity. Int. J. Appl. Comput. Math., 2019, 5(5): 128
Wazwaz A.M., El-Tantawy S.A., Solving the (3+1)-dimensional KP-Boussinesq and BKP-Boussinesq equations by the simplified Hirota’s method. Nonlinear Dynam., 2017, 88(4): 3017–3021
Xia J.W., Zhao Y.W., Lü X., Predictability, fast calculation and simulation for the interaction solution to the cylindrical Kadomtsev–Petviashvili equation. Commun. Nonlinear Sci. Numer. Simul., 2020, 90: 105260
Yajima N., Oikawa M., Satsuma J., Interaction of ion-acoustic solitons in three-dimensional space. J. Phys. Soc. Jpn., 1978, 44(5): 1711–1714
Yan X.W., Tian S.F., Dong M.J., Zou L., Bäacklund transformation, rogue wave solutions and interaction phenomena for a (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Nonlinear Dynam., 2018, 92: 709–720
Yang J.Y., Ma W.X., Abundant interaction solutions of the KP equation. Nonlinear Dynam., 2017, 89(2): 1539–1544
Yin M.Z., Zhu Q.W., Lü X., Parameter estimation of the incubation period of COVID-19 based on the doubly interval-censored data model, Nonlinear Dynam., 2021, 106: 1347–1358
Yin Y.H., Chen S.J., Lü X., Localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations. Chin. Phys. B, 2020, 29(12): 120502
Yin Y.H., Lü X., Ma W.X., Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+1)-dimensional nonlinear evolution equation. Nonlinear Dynam., 2022, 108: 4181–4194
Ze F., Hershkowitz N., Chan C., Lonngren K.E., Inelastic collision of spherical ion-acoustic solitons. Phys. Rev. Lett., 1979, 42(26): 1747–1750
Zhou Y., Ma W.X., Applications of linear superposition principle to resonant solitons and complexitons. Comput. Math. Appl., 2017, 73(8): 1697–1706
Acknowledgements
This work was supported by the Fundamental Research Funds for the Central Universities of China (No. 2022JBMC034), the National Natural Science Foundation of China (No. 12275017), and the Beijing Laboratory of National Economic Security Early-warning Engineering, Beijing Jiaotong University.
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Chen, S., Lü, X. & Yin, Y. Abundant Resonant Behaviors of Soliton Solutions to the (3+1)-dimensional BKP-Boussinesq Equation. Front. Math 18, 717–729 (2023). https://doi.org/10.1007/s11464-021-0050-6
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DOI: https://doi.org/10.1007/s11464-021-0050-6