Symmetry analysis and exact solutions of extended Kadomtsev-Petviashvili equation in fluids

[1] N. Kadkhoda, H. Jafari, Kudryshov method for solutions of isothermal magnetostatic atmospheres, Iranian Journal of Numerical Analysis and Optimization, 6 (2016) 43-52 Search in Google Scholar

[2] A. Sjöberg, Double reduction of PDEs from the association of symmetries with conservation laws with applications, Applied Mathematics and Computation 184 (2007) 608-616. Search in Google Scholar

[3] L.D. Moleleki, T. Motsepaa, C.M. Khalique, Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa equation, Applied Mathematics and Nonlinear Sciences 3(2) (2018) 459-474. Search in Google Scholar

[4] N. A. Kudryashov, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos, Solitons and Fractals, vol. 24, no. 5, pp. 1217-1231, 2005 Search in Google Scholar

[5] K.O. Alweil, K.A. Gepreel, T.A. Nofal, Simplest equation method for nonlinear evolution equations in mathematical physics, WSEAS Transactions on Mathematics 15 (2016) 2224-2880. Search in Google Scholar

[6] M.R. Alharthi, R.A. Alotabi, K.A. Gepreel, M.S. Mohamed, Homotopy Analysis Transform Method for Integro-Differential Equations, General Mathematics Notes 32 (2016) 32-48. Search in Google Scholar

[7] N.S. Al-Sayali, K.A. Gepreel, T.A. Nofal, Direct method for solving nonlinear strain wave equation in microstructure solids, International Journal of Physical Sciences 11 (2016) 121-131. Search in Google Scholar

[8] D. Baleanu, N. Kadkhoda, H. Jafari, G. M. Moremedi, Optimal system and symmetry reduction of the (1+1) dimensional Sawada-Kotera equation, Internatonal Journal of Pure and Applied Mathematics 108(2) (2016) 215-226. Search in Google Scholar

[9] M. Azadi, H. Jafari, H. G. Sun, Lie symmetry reductions of coupled KdV system of fractional order, Nonlinear Dynamics and Systems Theory, 18(1) (2018) 22-28. Search in Google Scholar

[10] G.W. Bluman, S. Kumei,Symmetries and differential equations, Springer-Verlag, New York (1989). Search in Google Scholar

[11] P.J. Olver, Applications of lie group to differential equations, second ed, Springer-Verlag (1993). Search in Google Scholar

[12] N.H. Ibragimov, Elemetary lie group analysis and ordinary differential equations, John Wiley & Sons, New York (1999). Search in Google Scholar

[13] H. Steudel, Uber die zuordnung zwischen invarianzeigenschaften und erhaltungssatzen, Zeitschrift fr Naturforschung, 17A (1962) 129-132. Search in Google Scholar

[14] A. Sjöberg, Double reduction of partial differential equations from the association of symmetries with conservation laws with application, Applied Mathematics and Computation, 184 (2007) 608-616. Search in Google Scholar

[15] S.C. Anco, G.W. Bluman, Direct construction method for conservation laws of partial differential equations. Part I: Examples of conservation law classifications, European Journal of Applied Mathematics, 13 (2002) 545-566. Search in Google Scholar

[16] A.H. Kara, F.M. Mahomed, Relationship between symmetries and conservation laws, International Journal Theoretical Physics, 39 (2000) 23-40. Search in Google Scholar

[17] L.D. Moleleki, C.M. Khalique, Symmetries, traveling wave solutions and conservation laws of a (3+1)-dimensional Boussinesq equation, Advances in Mathematical Physics, vol. 2014, Article ID 672679, 8 pages, 2014. Search in Google Scholar

[18] L.D. Moleleki, Solutions and conservation laws of a generalized 3D Kawahara equation, Europian Physical Journal Plus 133, 496 (2018). Search in Google Scholar

[19] M. Kumar, A.K. Tiwari, R. Kumar, Some more solutions of Kadomtsev-Petviashvili equation, Computers and Mathematics with Applications 74 (2017) 2599-2607. Search in Google Scholar

[20] Y. Ma, A. Wazwazb, B. Li, Novel bifurcation solitons for an extended Kadomtsev-Petviashvili equation in fluids, Physics letter A 413 (2021) 127585. Search in Google Scholar

[21] N. K. Vitanov, On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDEs: The role of the simples equation, Communications in Nonlinear Science and Numerical Simulation 16 (2011) 4215-4231. Search in Google Scholar