THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

Authors of this Paper

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Yanni Zhang

,

Xin Zhao

,

Jing Pang

online first only

Lump solutions for the dimensionally reduced variable coefficient B-type Kadomtsev-Petviashvili equation

ABSTRACT
Based on Hirota bilinear formulation, the lump solutions to dimensionally reduced generalized variable coefficient B-type Kadomtsev-Petviashvili equation are obtained. The solution process is figured out and the solution properties are illustrated graphically. The present method can be extended to other nonlinear equations.
KEYWORDS
Hirota bilinear form, generalized variable coefficient B-type Kadomtsev-Petviashvili equation, Lump solution
PAPER SUBMITTED: 2020-04-10
PAPER REVISED: 2020-06-18
PAPER ACCEPTED: 2020-06-18
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200410039Z
REFERENCES
  1. He, J.H. Exp-function Method for Fractional Differential Equations, International Journal of Nonlinear Sciences and Numerical Simulation, 14(2013), 6, pp. 363-366
  2. Ablowitz M.J., Clarkson P.A., Solitions, Nonlinear Evolution Equations and Inverse Scattering, Cambridge, Cambridge University Press, (1991)
  3. Ji, F.Y., et al. A fractal Boussinesq equation for nonlinear transverse vibration of a nanofiber-reinforced concrete pillar, Applied Mathematical Modelling, 82(2020), June, pp. 437-448
  4. He, J.H., et al. Difference equation vs differential equation on different scales, International Journal of Numerical Methods for Heat and Fluid Flow. 2020, DOI: 10.1108/HFF-03-2020-0178
  5. He, J.H. Asymptotic Methods for Solitary Solutions and Compactons. Abstract and Applied Analysis, 2012, Article Number: 916793
  6. Bekir A.,Painlevé test for some (2+1)-dimensional nonlinear equations, Chaos Solitons and Fractals, 32(2007), Feb.,pp.449-455
  7. Matveeev V.B., Salle MA, Darboux Transformations and Solitions, Berlin,Springers,( 1991)
  8. Hirota R., The direct method in solition theory, Cambridge,Cambridge University Press, (2004)
  9. Xing L., Ma W.X., Khalique C.M., A direct bilinear Backlund transformation of a (2+1)-dimensional Korteweg-de Vries-like model, Applied Mathematics Letters, 50(2015),pp.37-42
  10. Ma W.X., Trilinear equations, Bell polynomials, and resonant solutions , Frontiers of Mathematics in China, 8 ( 2013), pp. 1139-1156
  11. Wang, Y., Dong, Z. Z., Symmetry of a (2+1)-D System, Thermal Science, 22 (2018), Apr., pp. 1811-1822
  12. Zhang H., A note on exact complex travelling wave solutions for (2+1)-dimensional B-type Kadomtsev-Petviashvili equation , Applied Mathematics and Computation, 216(2010),pp. 2771-2777
  13. Yue, Y.F., Huang, L.L., Chen, Y., Localized waves and interaction solutions to an extended (3+1)-dimensional Jimbo-Miwa equation. Appl. Math. Lett. 89(2019), 70-77
  14. Ma W.X., Lump solutions to the Kadomtsev-Petviashvili equation , Physics Letters A, 379(2015) ,pp.1975-1978
  15. Hu, C.C., Tian, B., Wu, X.Y., Yuan, Y.Q., Du, Z., Mixed lump-kink and rogue wave-kink solutions for a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics. Eur. Phys. J. Plus 133 (2018)
  16. Hu, C.C., Tian, B., Yin, H.M., Zhang, C.R., Zhang, Z.,Dark breather waves, dark lump waves and lump wave soliton interactions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid. Comput. Math.Appl. 78(2019), 166-177
  17. Gao X.Y., Backlund transformation and shock-wave-type solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid mechanics , Ocean Engineering, 96(2015), pp.245-247
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Lump solutions for the dimensionally reduced variable coefficient B-type Kadomtsev-Petviashvili equation