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Research Article

Higher-order breather, lump and hybrid solutions of (2 + 1)-dimensional coupled nonlinear evolution equations with time-dependent coefficients

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Pages 1860-1876 | Received 13 Feb 2023, Accepted 18 May 2023, Published online: 05 Jun 2023

References

  • W. Yu, Q. Zhou, and M. Mirzazadeh, Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics. J. Adv. Res. 15 (2019), pp. 69–76.
  • W. Yu, M. Ekici, and M. Mirzazadeh, Periodic oscillations of dark solitons in nonlinear optics. Optik 165 (2018), pp. 341–344.
  • G. Yel, H.M. Baskonus, and W. Gao, New dark-bright soliton in the shallow water wave model. Aims Math. 5 (2020), pp. 4027–4044.
  • X. Zhao, B. Tian, and Q.X. Qu, KadomtsevCPetviashvili hierarchy reduction, soliton and semi-rational solutions for the (3 + 1)-dimensional generalized variable-coefficient shallow water wave equation in a fluid. Int. J. Comput. Math. 99(3) (2022), pp. 407–425.
  • X.Y. Gao, Y.J. Guo, and W.R. Shan, Bilinear forms through the binary Bell polynomials, N solitons and Bäcklund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beach. Commun. Theor. Phys. 72 (2020), pp. 095002.
  • F.Y. Liu, Y.T. Gao, and X. Yu, Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics. Chaos Soliton. Fract. 144 (2021), pp. 110559.
  • Y. Shen, B. Tian, and S.H. Liu, Bilinear Bäcklund transformation, soliton and breather solutions for a (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics. Phys. Scr 96 (2021), pp. 075212.
  • J. Zhao, J. Manafian, and N.E. Zaya, Multiple rogue wave, lump-periodic, lump-soliton, and interaction between k-lump and k-stripe soliton solutions for the generalized KP equation. Math. Methods Appl. Sci. 44 (2021), pp. 5079–5098.
  • Z. Zhang, B. Li, and A.M. Wazwaz, Lump molecules in fluid systems: Kadomtsev-Petviashvili I case. Phys. Lett. A 424 (2022), pp. 127848.
  • W. Chen, R. Guan, and M. Dong, N-solitons, lump solution and interaction phenomenon to the Boussinesq equation. Int. J. Comput. Math. 99(11) (2022), pp. 2237–2249.
  • G.Q. Meng, and H.C. Guo, Mixed solutions for an AB system in geophysical fluids or nonlinear optics. Appl. Math. Lett. 124 (2022), pp. 107632.
  • L.Q. Li, Y.T. Gao, and X. Yu, Bilinear forms, bilinear Bäcklund transformation, soliton and breather interactions of a damped variable-coefficient fifth-order modified Korteweg –de Vries equation for the surface waves in a strait or large channel. Chin. J. Phys. 77 (2022), pp. 915–926.
  • A.M. Wazwaz, Painlevé analysis for higher-dimensional integrable shallow water waves equations with time-dependent coefficients. Rom. Rep. Phys. 72 (2020), pp. 110.
  • Y. Shen, B. Tian, and S.H. Liu, Studies on certain bilinear form, N-soliton, higher-order breather, periodic-wave and hybrid solutions to a (3 + 1)-dimensional shallow water wave equation with time-dependent coefficients. Nonlinear Dyn. 108 (2022), pp. 2447–2460.
  • P.F. Han, and T. Bao, Novel hybrid-type solutions for the (3 + 1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients. Nonlinear Dyn. 107 (2022), pp. 1163–1177.
  • Z. Zhang, Z. Qi, and B. Li, Fusion and fission phenomena for (2 + 1)-dimensional fifth-order KdV system. Appl. Math. Lett. 116 (2021), pp. 107004.
  • Z. Zhao, and L. He, Resonance Y-type soliton and hybrid solutions of a (2 + 1)-dimensional asymmetricalNizhnik–Novikov–Veselov equation. Appl. Math. Lett. 122 (2021), pp. 107497.
  • A.H. Chen, and F.F. Wang, Fissionable wave solutions, lump solutions and interactional solutions for the (2 + 1)-dimensional Sawada–Kotera equation. Phys. Scr. 94 (2019), pp. 055206.
  • F.F. Ge, and S.F. Tian, Mechanisms of nonlinear wave transitions in the (2 + 1)-dimensional generalized breaking soliton equation. Nonlinear Dyn. 105 (2021), pp. 1753–1764.
  • W. Tan, Evolution of breathers and interaction between high-order lump solutions and N-solitons () for breaking soliton system. Phys. Lett. A 383 (2019), pp. 125907.
  • Y. Shen, and B. Tian, Bilinear auto-Bäcklund transformations and soliton solutions of a (3 + 1)-dimensional generalized nonlinear evolution equation for the shallow water waves. Appl. Math. Lett. 122 (2021), pp. 107301.
  • X. Lu, Y.F. Hua, and S.J. Chen, 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. 95 (2021), pp. 105612.
  • Y. Shen, B. Tian, and X. Zhao, Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions for a (3 + 1)-dimensional generalised Yu–Toda –Sasa –Fukuyama equation in a two-layer liquid or a lattice. Pramana 95 (2021), pp. 1–8.
  • X.J. He, and X. L, M-lump solution, soliton solution and rational solution to a (3 + 1)-dimensional nonlinear model. Math. Comput. Simulat. 197 (2022), pp. 327–340.
  • D. Kumar, I. Raju, and G.C. Paul, Characteristics of lump-kink and their fission-fusion interactions, rogue, and breather wave solutions for a (3 + 1)-dimensional generalized shallow water equation. Int. J. Comput. Math. 99 (2022), pp. 714–736.
  • S.J. Chen, and X. Chen, Lump and lump-multi-kink solutions in the (3 + 1)-dimensions. Commun. Nonlinear. Sci. 109 (2022), pp. 106103.
  • R. Emerson, R. Chalmers, and C. Cederstrand, Some factors influencing the long-wave limit of photosynthesis. Proc. Natl. Acad. Sci. USA 43 (1957), pp. 133.
  • X.J. He, and X. Lu, M-lump solution, soliton solution and rational solution to a (3 + 1)-dimensional nonlinear model. Math. Comput. Simulat. 197 (2022), pp. 327–340.
  • K. Bi, H.Q. Hao, and J.W. Zhang, Soliton, breather-like and dark-soliton-breather-like solutions for the coupled long-wave–short-wave system. Nonlinear Dyn. 108(1) (2022), pp. 543–554.
  • S. Singh, Similarity solutions for strong magnetogasdynamic cylindrical shock wave in rotating axisymmetric ideal gas with radiation heat flux using Lie group theoretic method. Ric. Mat. 69 (2022), pp. 1–23.
  • F.Y. Liu, Y.T. Gao, and X. Yu, Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics. Chaos Soliton. Fract. 144 (2021), pp. 110559.
  • W. Tan, W. Zhang, and J. Zhang, Evolutionary behavior of breathers and interaction solutions with M-solitons for (2 + 1)-dimensional KdV system. Appl. Math. Lett. 101 (2020), pp. 106063.
  • M.J. Li, H.P. Dai, and X.D. Wei, Some new soliton solutions and dynamical behaviours of (3 + 1)-dimensional Jimbo-Miwa equation. Int. J. Comput. Math. 99(8) (2021), pp. 1654–1668.
  • W.H. Zhu, F.Y. Liu, and J.G. Liu, Nonlinear dynamics for different nonautonomous wave structures solutions of a (4 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluid mechanics. Nonlinear Dyn. 108(4) (2022), pp. 4171–4180.
  • H. Ma, Y. Gao, and A. Deng, Fission and fusion solutions of the (2 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation: case of fluid mechanics and plasma physics. Nonlinear Dyn. 108(4) (2022), pp. 4123–4137.
  • H.F. Ismael, H.M. Baskonus, and H. Bulut, Instability modulation and novel optical soliton solutions to the GerdjikovCIvanov equation with M-fractional. Opt. Quantum Electron. 55(4) (2023), pp. 303–315.
  • Q. Li, W. Shan, and P. Wang, Breather, lump and N-soliton wave solutions of the (2 + 1)-dimensional coupled nonlinear partial differential equation with variable coefficients. Commun. Nonlinear. Sci. 106 (2022), pp. 106098.
  • B. Ren, W.X. Ma, and J. Yu, Characteristics and interactions of solitary and lump waves of a (2 + 1)-dimensional coupled nonlinear partial differential equation. Nonlinear Dyn. 96 (2019), pp. 717–727.
  • F. Yuan, Y. Cheng, and J. He, Degeneration of breathers in the Kadomttsev–Petviashvili I equation. Commun. Nonlinear. Sci. 83 (2020), pp. 105027.

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