Abundant Resonant Behaviors of Soliton Solutions to the (3+1)-dimensional BKP-Boussinesq Equation

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.

Keywords

Resonant soliton solutions / the (3+1)-dimensional BKP-Boussinesq equation / fusion / fission

References

[1] ChenSJ, LüX. Novel evolutionary behaviors of the mixed solutions to a generalized Burgers equation with variable coefficients. Commun. Nonlinear Sci. Numer. Simul., 2021, 95: 105628

[2] ChenSJ, LüX. Lump and lump-multi-kink solutions in the (3+1)-dimensions. Commun. Nonlinear Sci. Numer. Simul., 2022, 109: 106103

[3] ChenSJ, LüX, LiMG, WangF. Derivation and simulation of the M-lump solutions to two (2+1)-dimensional nonlinear equations. Phys. Scr., 2021, 96(9): 095201

[4] ChenSJ, LüX, MaWX. 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

[5] ChenSJ, YinYH, LüX. Elastic collision between one lump wave and multiple stripe waves of nonlinear evolution equations. Commun. Nonlinear Sci. Numer. Simul., 2023, 112: 107205

[6] GaoB, ZhangY. Exact solutions and conservation laws of the (3+1)-dimensional B-Type Kadomstev–Petviashvili(BKP)–Boussinesq Equation. Symmetry, 2020, 12(1): 97

[7] HirotaRThe Direct Method in Soliton Theory, 2004, Cambridge, Cambridge University Press

[8] HirotaR, ItoM. Resonance of solitons in one dimension. J. Phys. Soc. Japan, 1983, 52(3): 744-748

[9] HuH, LuY. Lie group analysis and invariant solutions of (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Modern Phys. Lett. B, 2020, 34(11): 2050106

[10] KaurL, WazwazAM. Painlevé analysis and invariant solutions of generalized fifth-order nonlinear integrable equation. Nonlinear Dynam., 2018, 94: 2469-2477

[11] KaurL, WazwazAM. Bright-dark lump wave solutions for a new form of the (3+1)-dimensional BKP-Boussinesq equation. Rom. Rep. Phys., 2019, 71(1): 102

[12] LiuB, ZhangXE, WangB, LüX. Rogue waves based on the coupled nonlinear Schröodinger option pricing model with external potential. Modern Phys. Lett. B, 2022, 36(15): 2250057

[13] LiuWH, ZhangYF. Dynamics of localized waves and interaction solutions for the (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Adv. Difference Equ., 2020, 2020: 93

[14] LüX, ChenSJ. 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

[15] LüX, ChenSJ. New general interaction solutions to the KPI equation via an optional decoupling condition approach. Commun. Nonlinear Sci. Numer. Simul., 2021, 103: 105939

[16] LüX, HuaYF, ChenSJ, TangXF. 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

[17] LüX, HuiHW, LiuFF, BaiYL. Stability and optimal control strategies for a novel epidemic model of COVID-19. Nonlinear Dynam., 2021, 106: 1491-1507

[18] MaWX. N-soliton solutions and the Hirota conditions in (2+1)-dimensions. Opt. Quant. Electron., 2020, 52: 511

[19] MaWX. N-soliton solution of a combined pKP-BKP equation. J. Geom. Phys., 2021, 165: 104191

[20] MaWX. N-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation. Math. Comput. Simulation, 2021, 190: 270-279

[21] MaWX. N-soliton solutions and the Hirota conditions in (1+1)-dimensions. Int. J. Nonlinear Sci. Numer. Simul., 2022, 23(1): 123-133

[22] MaWX, FanEG. Linear superposition principle applying to Hirota bilinear equations. Comput. Math. Appl., 2011, 61(4): 950-959

[23] MaWX, YongXL, LüX. Soliton solutions to the B-type Kadomtsev–Petviashvili equation under general dispersion relations. Wave Motion, 2021, 103: 102719

[24] MaWX, ZhangY, TangYN, TuJY. Hirota bilinear equations with linear subspaces of solutions. Appl. Math. Comput., 2012, 218(13): 7174-7183

[25] NikitenkovaSP, KovriguineDA. Stationary multi-wave resonant ensembles in a micro-tubule. Commun. Nonlinear Sci. Numer. Simul., 2019, 67: 314-333

[26] RahmonovIR, TekicJ, MaliP, IrieA, PlecenikA, ShukrinovYM. Resonance phenomena in an annular array of underdamped Josephson junctions. Phys. Rev. B, 2020, 101(17): 174515

[27] SoomereT, JüriE. Weakly two-dimensional interaction of solitons in shallow water. Eur. J. Mech. B Fluids, 2006, 25(5): 636-648

[28] SreekumarJ, NandakumaranVM. Soliton resonances in helium films. Phys. Lett. A, 1985, 112(3–4): 168-170

[29] VermaP, KaurL. Analytic study of (3+1)-dimensional Kadomstev–Petviashvili–Boussinesq equation: Painlevé analysis and exact solutions. Proceedings of the International Conference on Frontiers in Industrial and Applied Mathematics, 1975, 2018, Melville, NY, AIP Publishing: 030022

[30] VermaP, KaurL. 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

[31] VermaP, KaurL. Solitary Wave Solutions for (1+2)-dimensional nonlinear Schrödinger equation with dual power law nonlinearity. Int. J. Appl. Comput. Math., 2019, 5(5): 128

[32] WazwazAM, El-TantawySA. Solving the (3+1)-dimensional KP-Boussinesq and BKP-Boussinesq equations by the simplified Hirota’s method. Nonlinear Dynam., 2017, 88(4): 3017-3021

[33] XiaJW, ZhaoYW, LüX. Predictability, fast calculation and simulation for the interaction solution to the cylindrical Kadomtsev–Petviashvili equation. Commun. Nonlinear Sci. Numer. Simul., 2020, 90: 105260

[34] YajimaN, OikawaM, SatsumaJ. Interaction of ion-acoustic solitons in three-dimensional space. J. Phys. Soc. Jpn., 1978, 44(5): 1711-1714

[35] YanXW, TianSF, DongMJ, ZouL. 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

[36] YangJY, MaWX. Abundant interaction solutions of the KP equation. Nonlinear Dynam., 2017, 89(2): 1539-1544

[37] YinMZ, ZhuQW, LüX. Parameter estimation of the incubation period of COVID-19 based on the doubly interval-censored data model. Nonlinear Dynam., 2021, 106: 1347-1358

[38] YinYH, ChenSJ, LüX. Localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations. Chin. Phys. B, 2020, 29(12): 120502

[39] YinYH, LüX, MaWX. Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+1)-dimensional nonlinear evolution equation. Nonlinear Dynam., 2022, 108: 4181-4194

[40] ZeF, HershkowitzN, ChanC, LonngrenKE. Inelastic collision of spherical ion-acoustic solitons. Phys. Rev. Lett., 1979, 42(26): 1747-1750

[41] ZhouY, MaWX. Applications of linear superposition principle to resonant solitons and complexitons. Comput. Math. Appl., 2017, 73(8): 1697-1706

RIGHTS & PERMISSIONS

Peking University