Lie group analysis, exact solutions and conservation laws of (3+1) dimensional a B-type KP equation

In this study, we considered the (3+1) dimensional a B-type Kademtsev-Petviashvili (KP) equation. Using the Lie group analysis, the symmetry reductions and exact analytic solutions were obtained. Traveling wave solutions were also deduced. Lastly, local conservation laws were constructed by using the multiplier and Ibragimov’s nonlocal conservation method.

Keywords:

Lie symmetry, exact solution conservation laws,

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M. T. Darvishi, M. Najafi, S. Arbabi, L. Kavitha, Exact propagating multi-anti-kink soliton solutions of a (3+ 1)-dimensional B-type Kadomtsev–Petviashvili equation, Nonlinear Dynamics, 83(3) (2016), 1453-1462
L. Na, Bäcklund transformation and multi-soliton solutions for the (3+ 1)-dimensional BKP equation with Bell polynomials and symbolic computation, Nonlinear Dynamics, 82 (2015), 311-318.
W. X. Ma, E.G. Fan, Linear superposition principle applying to Hirota bilinear equations, Comput. Math. Appl, 61 (2011), 950–959
W. X. Ma, Z. Zhu, Solving the (3+ 1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm, Appl. Math. Comput, 218 (2012), 11871–11879
G.Q. Xu, X.Z. Huang, New variable separation solutions for two nonlinear evolution equations in higher dimensions, Chin. Phys. Lett., 30 (2013),130202
E. T. Bell, Exponential polynomials, Ann. Math., 35 (1934), 258–277
C. Gilson, F. Lambert, J. Nimmo, R. Willox, On the combinatorics of the Hirota D-operators, Proc. R. Soc. Lond. Ser. A, 452, (1996), 223–234
A. Biswas,1-Soliton solution of the generalized Camassa-Holm Kadomtsev-Petviashvili equation, Communications in Nonlinear Science and Numerical Simulation, 14 (6), 2524-2527. (2009).
A. Biswas, A. Ranasinghe, 1-Soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity, Applied Mathematics and Computation, 214 (2), 645-647. (2009).
A. Biswas, A. Ranasinghe,Topological 1-Soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity, Applied Mathematics and Computation, 217(4), 1771-1773. (2010).
A.J.M.Jawad, M Petkovic, A. Biswas, Soliton solutions for nonlinear Calogero-Degasperis and Potential Kadomtsev-Petviashvili equation, Computers and Mathematics with Applications,62 (6), 2621-2628. (2011).
H.Triki,B. J. M. Sturdevant, T. Hayat, Omar M. Aldossary, Anjan Biswas, Shock wave solutions of the variants of Kadomtsev-Petviashvili equation, Canadian Journal of Physics, Volume 89, Number 9, 979-984. (2011).
G. Ebadi, N. Yousefzadeh, H. Triki , A. Biswas, Exact solutions of the (2+1) dimensional Camassa Holm Kadomtsev-Petviashvili equation,Nonlinear Analysis: Modelling and Control, 17 (3), 280-296. (2012).
A. H. Bhrawy, M. A. Abdelkawy, Sachin Kumar, Anjan Biswas, Solitons and other solutions to Kadomtsev-Petviashvili equation of B-type, Romanian Journal of Physics, 58 (7-8), 729-748. (2013).
G. Ebadi, N. Y. Fard, A. H. Bhrawy, S Kumar, H Triki, A Yildirim, Anjan Biswas, Solitons and other solutions to the (3+1) dimensional extended Kadomtsev-Petviashvili equation with power law nonlinearity, Romanian Reports in Physics, 65 (1), 27-62. (2013).
S. Kumar, E. Zerrad, A Yildirim, A. Biswas.The Kadomtsev-Petviashvili equation-Burgers equation with power law nonlinearity in dust plasmas ,Proceedings of the Romanian Academy, Series A, 14(3), 204-210. (2013).
N. Y. Fard, M R. Foroutan, M Eslami, M Mirzazadeh, A Biswas, Solitary waves and other solutions to Kadomtsev-Petviashvili equation with spatio-temporal dispersion, Romanian Journal of Physics, 60 ( 9-10), 1337-1360. (2015).
A.J. M. Jawad, M Mirzazadeh, A Biswas, Dynamics of shallow water waves with Gardner Kadomtsev-Petviashvili equation, Discrete and Continuous Dynamical Systems, Series S, 8 ( 6), 1155-1164. (2015).
P.J. Olver, Applications of Lie groups to differential equations (Vol. 107), Springer Science & Business Media, 2000.
G. W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer New York, 1989.
G. W. Wang, X.Q. Liu, Y.Y. Zhang, Symmetry reduction, exact solutions and conservation laws of a new fifth-order nonlinear integrable equation. Communications in Nonlinear Science and Numerical Simulation,18(9) (2013), 2313-2320.
A.R. Adem, C.M. Khalique, A. Biswas, Solutions of Kadomtsev–Petviashvili equation with power law nonlinearity in 1+ 3 dimensions. Mathematical Methods in the Applied Sciences, 34(5) (2011), 532-543.
G. Wang, K. Fakhar, Lie symmetry analysis, nonlinear self-adjointness and conservation laws to an extended (2+ 1)-dimensional Zakharov–Kuznetsov–Burgers equation, Computers & Fluids, 119,(2015),143-148
A. Cheviakov, GeM software package for computation of symmetries and conservation laws of differential equations. Comp. Phys. Comm. 176 (2007), 48-61
N.H. Ibragimov, A new conservation theorem, J Math Anal Appl, 333 (2007), 311–28.
N.H. Ibragimov, Nonlinear self-adjointness and conservation laws, J Phys A: Math Theor, 44 (2011) 432002.
E. Yaşar, T. Özer, Conservation laws for one-layer shallow water wave systems, Nonlinear Analysis: Real World Applications, 11(2) (2010), 838-848.
E. Yaşar, T. Özer, Invariant solutions and conservation laws to nonconservative FP equation, Computers & Mathematics with Applications, 59(9) (2010), 3203-3210.
E. Yaşar, T. Özer, On symmetries, conservation laws and invariant solutions of the foam-drainage equation, International Journal of Non-Linear Mechanics, 46(2) (2011), 357-362.