THERMAL SCIENCE

International Scientific Journal

Pin-Xia Wu

,

Yu-Feng Zhang

,

Qi-Qi Yin

,

Yan Wang

INTEGRABILITY AND LUMP-TYPE SOLUTIONS TO THE 3-D KADOMTSEV-PETVIASHVILI-BOUSSINESQ-LIKE EQUATION

ABSTRACT
The (3+1)-D Kadomtsev-Petviashvili-Boussinesq-like equation is studied, and its bilinear form, Backlund transformation and Lax pairs are elucidated. Lump-type solutions are obtained, which include periodic lump and interaction lump solutions, through the three-wave method and the ansatz method. The dynamic evolution mechanisms of solutions are illustrated graphically.
KEYWORDS
bilinear form, Backlund transformation, Lax pairs, periodic lump solutions, interaction lump solutions
PAPER SUBMITTED: 2018-05-10
PAPER REVISED: 2018-07-02
PAPER ACCEPTED: 2018-08-28
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904373W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE No. 4, PAGES [2373 - 2380]
REFERENCES
[1] Yang, J. Y., Ma, W. X., Abundant Interaction Solutions of the KP Equation. Non-linear Dynam, 89 (2017), 2, pp. 1539-1544
[2] Zhang, Y. F., Ma, W. X., Rational Solutions to a KdV-Like Equation, Applied Mathematics and Compu-tation, 256 (2015), Apr., pp. 252-256
[3] Zhang, Y. F., Ma, W. X., A Study on Rational Rolutions to a KP-Like Equation, Zeitschrift für Naturforschung A, 70 (2015), 4, pp. 263-268
[4] Wang, Y., et al., An Explanation of Local Fractional Variational Iteration Method and its Application to Local Fractional Modified Korteweg-de Vries Equation. Thermal Science, 22 (2018), 1, pp. 23-27
[5] Wang, Y., et al., A Short Review on Analytical Methods for Fractional Equations with He's Fractional Derivative, Thermal Science, 21 (2017), 4, pp. 1567-1574
[6] Li, Y., et al., Darboux Transformations of Classical Boussinesq System and its New Solutions. Physics Letters A, 275 (2000), 1-2, pp. 60-66
[7] Lambert, F., Springael, J., Soliton Equations and Simple Combinatorics, Acta Appl. Math. 102 (2008), 2-3, pp. 147-178
[8] Zhao, Z. L., et al., Bäcklund Transformation and Solutions of a (3+1)-Dimensional Non-linear Evolution Equation. Applied Mathematics and Computation, 248 (2014), Dec., pp. 456-462
[9] Gao, X. Y., Bäcklund Transformation and Shock-Wave Type Solutions for a Generalized (3+1)-Dimen-sional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equation in Fluid Mechanics. Ocean Engi-neering, 96 (2015), Mar., pp. 245-247
[10] Huang, Q. M., et al., Bilinear Bäcklund Transformation, Soliton and Periodic Wave Solutions for a (3+1)-Dimensional Variable-Coefficient Generalized Shallow Water Wave Equation, Non-linear Dy-namics, 87 (2017), 4, pp. 2529-2540
[11] Lan, Z. Z., et al., Solitons, Bäcklund Transformation and Lax Pair for a (2+1)-D B-Type Kadomtsev-Petviashvili Equation in the Fluid/Plasma Mechanics, Modern Physics Letters B, 30 (2016), 25, ID 1650265
[12] Xiao, Z. J., et al., Multi-Soliton Solutions and Bäcklund Transformation for a Two-Mode KdV Equation in a Fluid. Waves in Random and Complex Media, 27 (2017), 1, pp. 1-14
[13] Zhang, Y. F., Tam, H., Discussion on Integrable Properties for Higher-Dimensional Variable-Coefficient Non-linear Partial Differential Equations. Journal of Mathematical Physics, 54 (2013), 1, ID 013516
[14] Lin, R., et al., Solving the KdV Hierarchy with Self-Consistent Sources by Inverse Scattering Method. Physica A: Statistical Mechanics and its Applications, 291 (2001), 1, pp. 287-298
[15] Zhou, Y., Ma, W. X., Complexiton Solutions to Soliton Equations by the Hirota Method. Journal of Mathematical Physics, 58 (2017), 10, ID 101511
[16] Ji, J. L., Zhu, Z. N., On a Nonlocal Modied Korteweg-de Vries Equation: Integrability, Darboux Trans-formation and Soliton Solutions, Communications in Non-linear Science and Numerical Simulation, 42 (2017), Jan., pp. 699-708
[17] Fan, E. G., Two New Applications of the Homogeneous Balance Method. Physics Letters A, 265 (2000), 5, pp. 353-357
[18] He, J.-H., Homotopy Perturbation Method: A New Non-linear Analytical Technique, Applied Mathemat-ics and computation, 135 (2003), 1, pp.73-79
[19] He, J.-H., Wu, X. H., Exp-Function Method for Non-linear Wave Equations, Chaos, Solitons & Frac-tals, 30 (2006), 3, pp. 700-708
[20] Wazwaz, A. M., El-Tantawy, S. A., Solving the (3+1)-Dimensional KP-Boussinesq and BKP-Boussi-nesq Equations by the Simplified Hirota's Method, Non-linear Dynamics, 88 (2017), 4, pp. 3017-3021
[21] Yu, J. P., Sun, Y. L., A Direct Bäcklund Transformation for a (3+1)-Dimensional Kadomtsev-Pet-viashvili-Boussinesq-Like Equation, Non-linear Dynamics, 90 (2017), 4, pp. 2263-2268
[22] Liu, J. G., et al., New Periodic Wave Solutions of (3+1)-Dimensional Soliton Equation, Thermal Sci-ence, 21 (2017), Suppl 1, pp. S169-S176
[23] Wu, P. X., et al., Lump, Periodic Lump and Interaction Lump Stripe Solutions to the (2+1)-Dimensional B-Type Kadomtsev-Petviashvili Equation, Modern Physics Letters B, 32 (2018), 7, ID 1850106
[24] Ma, W. X., et al., Lump-Type Solutions to Non-linear Differential Equations Derived from Generalized Bilinear Equations, International Journal of Modern Physics B, 30 (2016), 28-29, ID1640018
[25] Yong, X., et al., Lump Solutions to the Kadomtsev-Petviashvili I Equation with a Self-Consistent Source, Computers & Mathematics with Applications, 75 (2018), 9, pp. 3414-3419
PDF VERSION [DOWNLOAD]
Integrability and lump-type solutions to the 3-D Kadomtsev-Petviashvili-Boussinesq-like equation

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence