Similarity reductions on a \((2+1)\)-dimensional variable-coefficient modified Kadomtsev-Petviashvili system describing certain electromagnetic waves in a thin film. (English) Zbl 07879192
Summary: For the electromagnetic waves in an isotropic charge-free infinite thin film with the potential application in magneto-optic recording, we investigate a \((2+1)\)-dimensional variable-coefficient modified Kadomtsev-Petviashvili system. Under the help of symbolic computation, different from those in the existing literatures, we find two branches of the similarity reductions, able to reduce that system to a solvable ordinary differential equation.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76A20 | Thin fluid films |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 35C07 | Traveling wave solutions |
| 35C08 | Soliton solutions |
| 68W30 | Symbolic computation and algebraic computation |
| 37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
Keywords:
magneto-optics; \((2+1)\)-dimensional variable-coefficient modified Kadomtsev-Petviashvili system; similarity reductions; symbolic computationReferences:
| [1] | Magnetooptics, https://www.thefreedictionary.com/magnetooptics (2024) |
| [2] | Khater, MM, Analyzing pulse behavior in optical fiber: novel solitary wave solutions of the perturbed Chen-Lee-Liu equation, Mod. Phys. Lett. B, 37, 2350177, 2023 · doi:10.1142/S0217984923501774 |
| [3] | Khater, MM, Computational simulations of propagation of a tsunami wave across the ocean, Chaos Solitons Fract., 174, 2023 · doi:10.1016/j.chaos.2023.113806 |
| [4] | Khater, MM, Soliton propagation under diffusive and nonlinear effects in physical systems; \((1+1)\)-dimensional MNW integrable equation, Phys. Lett. A, 480, 2023 · Zbl 1527.35130 · doi:10.1016/j.physleta.2023.128945 |
| [5] | Khater, MM, Horizontal stratification of fluids and the behavior of long waves, Eur. Phys. J. Plus, 138, 715, 2023 · doi:10.1140/epjp/s13360-023-04336-z |
| [6] | Khater, MM, Characterizing shallow water waves in channels with variable width and depth; computational and numerical simulations, Chaos Solitons Fract., 173, 2023 · doi:10.1016/j.chaos.2023.113652 |
| [7] | Khater, MM, Advancements in computational techniques for precise solitary wave solutions in the \((1+1)\)-dimensional Mikhailov-Novikov-Wang equation, Int. J. Theor. Phys., 62, 152, 2023 · Zbl 1531.65212 · doi:10.1007/s10773-023-05402-z |
| [8] | Khater, MM, Numerous accurate and stable solitary wave solutions to the generalized modified Equal-Width equation, Int. J. Theor. Phys., 62, 151, 2023 · Zbl 1521.35075 · doi:10.1007/s10773-023-05362-4 |
| [9] | Khater, MM, Long waves with a small amplitude on the surface of the water behave dynamically in nonlinear lattices on a non-dimensional grid, Int. J. Mod. Phys. B, 37, 2350188, 2023 · doi:10.1142/S0217979223501886 |
| [10] | Khater, MM, Abundant and accurate computational wave structures of the nonlinear fractional biological population model, Int. J. Mod. Phys. B, 37, 2350176, 2023 · doi:10.1142/S021797922350176X |
| [11] | Cheng, CD; Tian, B.; Ma, YX; Zhou, TY; Shen, Y., Pfaffian, breather and hybrid solutions for a \((2+1)\)-dimensional generalized nonlinear system in fluid mechanics and plasma physics, Phys. Fluids, 34, 115132, 2022 · doi:10.1063/5.0119516 |
| [12] | Gao, XY, Oceanic shallow-water investigations on a generalized Whitham-Broer-Kaup-Boussinesq-Kupershmidt system, Phys. Fluids, 35, 127106, 2023 · doi:10.1063/5.0170506 |
| [13] | Gao, XY, Two-layer-liquid and lattice considerations through a \((3+1)\)-dimensional generalized Yu-Toda-Sasa-Fukuyama system, Appl. Math. Lett., 152, 109018, 2024 · Zbl 07850545 · doi:10.1016/j.aml.2024.109018 |
| [14] | Yin, Y.H., Lü, X., Jiang, R., Jia, B., Gao, Z.Y.: Kinetic analysis and numerical tests of an adaptive car-following model for real-time traffic in ITS. Physica A 635, 129494 (2024) · Zbl 07820912 |
| [15] | Gao, XY, Considering the wave processes in oceanography, acoustics and hydrodynamics by means of an extended coupled \((2+1)\)-dimensional Burgers system, Chin. J. Phys., 86, 572-577, 2023 · Zbl 1541.35014 · doi:10.1016/j.cjph.2023.10.051 |
| [16] | Peng, X., Zhao, Y.W., Lü, X.: Data-driven solitons and parameter discovery to the (2+1)-dimensional NLSE in optical fiber communications. Nonlinear Dyn. 112, 1291-1306 (2024) |
| [17] | 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. 130, 107205 (2024) · Zbl 1531.35248 |
| [18] | Chen, Y., Lü, X.: Wronskian solutions and linear superposition of rational solutions to B-type Kadomtsev-Petviashvili equation. Phys. Fluids 35, 106613 (2023) |
| [19] | Cao, F., Lü, X., Zhou, Y.X., Cheng, X.Y.: Modified SEIAR infectious disease model for Omicron variants spread dynamics. Nonlinear Dyn. 111, 14597-14620 (2023) |
| [20] | Liu, K.W., Lü, X., Gao, F., Zhang, J.: Expectation-maximizing network reconstruction and most applicable network types based on binary time series data. Physica D 454, 133834 (2023) · Zbl 1521.92090 |
| [21] | Yin, Y.H., Lü, X.: Dynamic analysis on optical pulses via modified PINNs: Soliton solutions, rogue waves and parameter discovery of the CQ-NLSE. Commun. Nonlinear Sci. Numer. Simul. 126, 107441 (2023) · Zbl 1528.35172 |
| [22] | Gao, D., Lü, X., Peng, M.S.: Study on the (2+1) dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation. Phys. Scr. 98, 095225 (2023) |
| [23] | Shen, Y.; Tian, B.; Zhou, TY; Cheng, CD, Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium, Chaos Solitons Fract., 171, 113497, 2023 · doi:10.1016/j.chaos.2023.113497 |
| [24] | Gao, XY; Guo, YJ; Shan, WR, Theoretical investigations on a variable-coefficient generalized forced-perturbed Korteweg-de Vries-Burgers model for a dilated artery, blood vessel or circulatory system with experimental support, Commun. Theor. Phys., 75, 115006, 2023 · Zbl 1537.76188 · doi:10.1088/1572-9494/acbf24 |
| [25] | Zhou, TY; Tian, B.; Shen, Y.; Cheng, CD, Lie symmetry analysis, optimal system, symmetry reductions and analytic solutions for a \((2+1)\)-dimensional generalized nonlinear evolution system in a fluid or a plasma, Chin. J. Phys., 84, 343-356, 2023 · Zbl 1541.35405 · doi:10.1016/j.cjph.2023.05.017 |
| [26] | Wu, XH; Gao, YT; Yu, X.; Li, LQ; Ding, CC, Vector breathers, rogue and breather-rogue waves for a coupled mixed derivative nonlinear Schrödinger system in an optical fiber, Nonlinear Dyn., 111, 5641-5653, 2023 · doi:10.1007/s11071-022-08058-2 |
| [27] | Raza, N.; Deifalla, A.; Rani, B.; Shah, NA; Ragab, AE, Analyzing Soliton Solutions of the (n \(+1)\)-dimensional generalized Kadomtsev-Petviashvili equation: comprehensive study of dark, bright, and periodic dynamics, Results Phys., 56, 2024 · doi:10.1016/j.rinp.2023.107224 |
| [28] | Khater, MM, Horizontal stratification of fluids and the behavior of long waves, Eur. Phys. J. Plus, 138, 715, 2023 · doi:10.1140/epjp/s13360-023-04336-z |
| [29] | Ma, YL; Wazwaz, AM; Li, BQ, New extended Kadomtsev-Petviashvili equation: multiple soliton solutions, breather, lump and interaction solutions, Nonlinear Dyn., 104, 1581-1594, 2021 · doi:10.1007/s11071-021-06357-8 |
| [30] | Ma, YL; Wazwaz, AM; Li, BQ, A new \((3+1)\)-dimensional Kadomtsev-Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves, Math. Comput. Simul., 187, 505-519, 2021 · Zbl 1540.35350 · doi:10.1016/j.matcom.2021.03.012 |
| [31] | Veerakumar, V.; Daniel, M., Modified Kadomtsev-Petviashvili (MKP) equation and electromagnetic soliton, Math. Comput. Simul., 62, 163-169, 2003 · Zbl 1015.78010 · doi:10.1016/S0378-4754(02)00176-3 |
| [32] | Zhou, TY; Tian, B.; Shen, Y.; Gao, XT, Bilinear form, bilinear auto-Bäcklund transformation, soliton and half-periodic kink solutions on the non-zero background of a \((3+1)\)-dimensional time-dependent-coefficient Boiti-Leon-Manna-Pempinelli equation, Wave Motion, 121, 2023 · Zbl 1524.35572 · doi:10.1016/j.wavemoti.2023.103180 |
| [33] | Zhou, TY; Tian, B.; Shen, Y.; Gao, XT, Auto-Bäcklund transformations and soliton solutions on the nonzero background for a \((3+1)\)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in a fluid, Nonlinear Dyn., 111, 8647-8658, 2023 · doi:10.1007/s11071-023-08260-w |
| [34] | Zhou, TY; Tian, B., Auto-Bäcklund transformations, Lax pair, bilinear forms and bright solitons for an extended \((3+1)\)-dimensional nonlinear Schrödinger equation in an optical fiber, Appl. Math. Lett., 133, 2022 · Zbl 1496.35374 · doi:10.1016/j.aml.2022.108280 |
| [35] | Cheng, C.D., Tian, B., Shen, Y., Zhou, T.Y.: Bilinear form, auto-Bäcklund transformations, Pfaffian, soliton, and breather solutions for a \((3+1)\)-dimensional extended shallow water wave equation. Phys. Fluids 35, 087123 (2023) |
| [36] | Feng, CH; Tian, B.; Yang, DY; Gao, XT, Lump and hybrid solutions for a \((3+1)\)-dimensional Boussinesq-type equation for the gravity waves over a water surface, Chin. J. Phys., 83, 515-526, 2023 · Zbl 1541.35377 · doi:10.1016/j.cjph.2023.03.023 |
| [37] | Shen, Y.; Tian, B.; Zhou, TY; Gao, XT, Extended \((2+1)\)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics: solitons, breathers, lumps and interactions, Eur. Phys. J. Plus, 138, 305, 2023 · doi:10.1140/epjp/s13360-023-03886-6 |
| [38] | Shen, Y.; Tian, B.; Cheng, CD; Zhou, TY, N-soliton, Mth-order breather, Hth-order lump, and hybrid solutions of an extended \((3+1)\)-dimensional Kadomtsev-Petviashvili equation, Nonlinear Dyn., 111, 10407-10424, 2023 · doi:10.1007/s11071-023-08369-y |
| [39] | Shen, Y.; Tian, B.; Cheng, CD; Zhou, TY, Pfaffian solutions and nonlinear waves of a \((3+1)\)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics, Phys. Fluids, 35, 2023 · doi:10.1063/5.0135174 |
| [40] | Shen, Y.; Tian, B.; Yang, DY; Zhou, TY, Hybrid relativistic and modified Toda lattice-type system: equivalent form, N-fold Darboux transformation and analytic solutions, Eur. Phys. J. Plus, 138, 744, 2023 · doi:10.1140/epjp/s13360-023-04331-4 |
| [41] | Wu, XH; Gao, YT, Generalized Darboux transformation and solitons for the Ablowitz-Ladik equation in an electrical lattice, Appl. Math. Lett., 137, 2023 · Zbl 1504.35124 · doi:10.1016/j.aml.2022.108476 |
| [42] | Wu, XH; Gao, YT; Yu, X.; Liu, FY, Generalized Darboux transformation and solitons for a Kraenkel-Manna-Merle system in a ferromagnetic saturator, Nonliner Dyn., 111, 14421-14433, 2023 · doi:10.1007/s11071-023-08510-x |
| [43] | Wu, XH; Gao, YT; Yu, X.; Ding, CC, \(N\)-fold generalized Darboux transformation and asymptotic analysis of the degenerate solitons for the Sasa-Satsuma equation in fluid dynamics and nonlinear optics, Nonlinear Dyn., 111, 16339-16352, 2023 · doi:10.1007/s11071-023-08533-4 |
| [44] | Gao, XT; Tian, B., Water-wave studies on a \((2+1)\)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system, Appl. Math. Lett., 128, 107858, 2022 · Zbl 1491.76013 · doi:10.1016/j.aml.2021.107858 |
| [45] | Gao, XY; Guo, YJ; Shan, WR, On the oceanic/laky shallow-water dynamics through a Boussinesq-Burgers system, Qual. Theory Dyn. Syst., 23, 57, 2024 · Zbl 1531.35322 · doi:10.1007/s12346-023-00905-w |
| [46] | El-Shiekh, RM; Gaballah, M., New analytical solitary and periodic wave solutions for generalized variable-coefficients modified KdV equation with external-force term presenting atmospheric blocking in oceans, J. Ocean Eng. Sci., 7, 372-376, 2022 · doi:10.1016/j.joes.2021.09.003 |
| [47] | Khater, MM, Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect, Int. J. Mod. Phys. B, 37, 2350083, 2023 · doi:10.1142/S0217979223500832 |
| [48] | Khater, MM, In surface tension; gravity-capillary, magneto-acoustic, and shallow water waves’ propagation, Eur. Phys. J. Plus, 138, 320, 2023 · doi:10.1140/epjp/s13360-023-03902-9 |
| [49] | Khater, MM, A hybrid analytical and numerical analysis of ultra-short pulse phase shifts, Chaos Solitons Fract., 169, 2023 · doi:10.1016/j.chaos.2023.113232 |
| [50] | Khater, MM, Prorogation of waves in shallow water through unidirectional Dullin-Gottwald-Holm model; computational simulations, Int. J. Mod. Phys. B, 37, 2350071, 2023 · doi:10.1142/S0217979223500716 |
| [51] | Khater, MM, In solid physics equations, accurate and novel soliton wave structures for heating a single crystal of sodium fluoride, Int. J. Mod. Phys. B, 37, 2350068, 2023 · doi:10.1142/S0217979223500686 |
| [52] | Khater, MM, Nonlinear elastic circular rod with lateral inertia and finite radius: dynamical attributive of longitudinal oscillation, Int. J. Mod. Phys. B, 37, 2350052, 2023 · doi:10.1142/S0217979223500522 |
| [53] | Khater, MM, Computational and numerical wave solutions of the Caudrey-Dodd-Gibbon equation, Heliyon, 9, 2023 · doi:10.1016/j.heliyon.2023.e13511 |
| [54] | Khater, MM, Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers, Chaos Solitons Fract., 167, 2023 · doi:10.1016/j.chaos.2022.113098 |
| [55] | Khater, MM, Physics of crystal lattices and plasma; analytical and numerical simulations of the Gilson-Pickering equation, Results Phys., 44, 2023 · doi:10.1016/j.rinp.2022.106193 |
| [56] | Khater, MM, Hybrid accurate simulations for constructing some novel analytical and numerical solutions of three-order GNLS equation, Int. J. Geom. Methods Mod. Phys., 20, 2350159, 2023 · Zbl 1532.35425 · doi:10.1142/S0219887823501591 |
| [57] | Zhu, ZN, Lax pair, Bäcklund transformation, solitary wave solution and finite conservation laws of the general KP equation and MKP equation with variable coefficients, Phys. Lett. A, 180, 409-412, 1993 · doi:10.1016/0375-9601(93)90291-7 |
| [58] | Gao, YT; Tian, B., On a variable-coefficient modified KP equation and a generalized variable-coefficient KP equation with computerized symbolic computation, Int. J. Mod. Phys. C, 12, 819-833, 2001 · doi:10.1142/S0129183101002024 |
| [59] | Gao, YT; Tian, B., Variable-coefficient balancing-act algorithm extended to a variable-coefficient MKP model for the rotating fluids, Int. J. Mod. Phys. C, 12, 1383-1389, 2001 · doi:10.1142/S0129183101002681 |
| [60] | Wang, X.; Wang, L., Darboux transformation and nonautonomous solitons for a modified Kadomtsev-Petviashvili equation with variable coefficients, Comput. Math. Appl., 75, 4201-4213, 2018 · Zbl 1420.35330 · doi:10.1016/j.camwa.2018.03.022 |
| [61] | Gao, XY; Guo, YJ; Shan, WR; Yin, HM; Du, XX; Yang, DY, Certain electromagnetic waves in a ferromagnetic film, Commun. Nonlinear Sci. Numer. Simul., 105, 2022 · Zbl 1497.35449 · doi:10.1016/j.cnsns.2021.106066 |
| [62] | Gao, XY; Guo, YJ; Shan, WR, Reflecting upon some electromagnetic waves in a ferromagnetic film via a variable-coefficient modified Kadomtsev-Petviashvili system, Appl. Math. Lett., 132, 2022 · Zbl 1504.35522 · doi:10.1016/j.aml.2022.108189 |
| [63] | Sun, ZY; Gao, YT; Yu, X.; Meng, XH; Liu, Y., Inelastic interactions of the multiple-front waves for the modified Kadomtsev-Petviashvili equation in fluid dynamics, plasma physics and electrodynamics, Wave Motion, 46, 511-521, 2009 · Zbl 1231.37045 · doi:10.1016/j.wavemoti.2009.06.014 |
| [64] | Wael, S., Seadawy, A.R., EL-Kalaawy, O.H., Maowad, S.M., Baleanu, D.: Symmetry reduction, conservation laws and acoustic wave solutions for the extended Zakharov-Kuznetsov dynamical model arising in a dust plasma. Results Phys. 19, 103652 (2020) |
| [65] | Ghose-Choudhury, A.; Garai, S., Solutions of the variable coefficient Radhakrishnan-Kundu-Lakshmanan equation using the method of similarity reduction, Optik, 241, 167254, 2021 · doi:10.1016/j.ijleo.2021.167254 |
| [66] | Clarkson, P.; Kruskal, M., New similarity reductions of the Boussinesq equation, J. Math. Phys., 30, 2201-2213, 1989 · Zbl 0698.35137 · doi:10.1063/1.528613 |
| [67] | Gao, XY; Guo, YJ; Shan, WR, Ultra-short optical pulses in a birefringent fiber via a generalized coupled Hirota system with the singular manifold and symbolic computation, Appl. Math. Lett., 140, 108546, 2023 · Zbl 1520.78040 · doi:10.1016/j.aml.2022.108546 |
| [68] | Cheng, CD; Tian, B.; Shen, Y.; Zhou, TY, Bilinear form and Pfaffian solutions for a \((2+1)\)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics, Nonlinear Dyn., 111, 6659-6675, 2023 · doi:10.1007/s11071-022-08189-6 |
| [69] | Shen, Y.; Tian, B.; Zhou, TY; Gao, XT, N-fold Darboux transformation and solitonic interactions for the Kraenkel-Manna-Merle system in a saturated ferromagnetic material, Nonlinear Dyn., 111, 2641-2649, 2023 · doi:10.1007/s11071-022-07959-6 |
| [70] | Cheng, CD; Tian, B.; Zhou, TY; Shen, Y., Wronskian solutions and Pfaffianization for a \((3+1)\)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation in a fluid or plasma, Phys. Fluids, 35, 037101, 2023 · doi:10.1063/5.0141559 |
| [71] | Ince, E., Ordinary Differential Equations, 1956, New York: Dover, New York · JFM 53.0399.07 |
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.
