International Journal of Nonlinear Analysis and Applications

Soliton solutions and other analytical solutions of a new (3+1)-dimensional novel KP like equation

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Botswana, Private Bag 22, Gaborone, Botswana

2 Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, Republic of South Africa

3 Department of Mathematical Sciences, University of South Africa, UNISA 0003, Republic of South Africa

Abstract

We study a new (3+1)-dimensional novel KP-like equation. We show that this equation admits topological soliton solutions. These will be attained via the aid of ansatz methods. Furthermore, mixed solutions consisting of singular and periodic solutions and others are derived. Moreover, other analytical solutions based on modern group analysis are derived.  In addition,  low-order conservation laws are constructed.

Keywords

[1] G.W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York Applied Mathematical Sciences, 1989.
[2] S.J. Chen and X. L¨u, Lump and lump-multi-kink solutions in the (3+1)-dimensions, Commun. Nonlinear Sci. Numer. Simul. 109 (2022), 106103.
[3] M.L. Gandarias and M.S. Bruzon, Some conservation laws for a forced KdV equation, Nonlinear Anal. Real World Appl. 13 (2012), no. 6, 2692–2700.
[4] M.L. Gandarias and M.S. Bruzon, Symmetry analysis and exact solutions of some Ostrovsky euqtions, Theoret Math. Phys. 168 (2011), no. 1, 898–911.
[5] M.L. Gandarias and M.S. Bruzon, Traveling wave solutions for a generalized Ostrovsky equation, Math. Meth. Appl. Sci. 41 (2018), no. 15, 5840–5850.
[6] X.J. He and X. L¨u, M-lump solution, soliton solution and rational solution to a (3+1)-dimensional nonlinear model, Math. Comput. Simulation 197 (2022), 327–340.
[7] N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Vol 1-3, CRC Press Boca Raton Florida, 1994-1996.
[8] C.K. Kuo and W.X. Ma, An effective approach for constructing novel KP-like equations, Waves Random Complex Media 32 (2022), no. 2, 629–640.
[9] R. Naz, F.M. Mahomed and D.P. Mason, Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics Appl. Math. Comput. 205 (2008), no. 1, 212–230.
[10] P.J. Olver, Applications of Lie Groups to Differential Equations, 2nd edition, Graduate Texts in Mathematics, Springer-Verlag, Berlin, 1993.
[11] H. Steudel, Uber die Zuordnung zwischen Invarianzeigenschaften und Erhaltungssatzen, Zeit. Naturforsch 17 (1962), no. 2, 129–132.
[12] H. Triki, A. Benlalli and A.M. Wazwaz, Exact solutions of the generalized Pochhammer-Chree equation with sixth-order dispersion, Roman. J. Phys. 60 (2015), 935–951.
[13] H. Triki and A.M. Wazwaz, Bright and dark soliton solutions for a K(m, n) equation with t-dependent coefficients, Phys. Lett. A 373 (2009), 2162–2165.
[14] A.M. Wazwaz, New (3 +1)-dimensional Date-Jimbo-Kashiwara-Miwa equations withconstant and time-dependent coefficients: Painlev´e integrability, Phys. Lett. A 384 (2020), 126787.
[15] Y. Yıldırım and E. Yasar, A (2+1)-dimensional breaking soliton equation: Solutions and conservation laws, Chaos Solitons Fractals 107 (2018), 146–155.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 1
January 2023
Pages 2623-2632
  • Receive Date: 17 June 2022
  • Accept Date: 14 January 2023