Symmetry reductions and exact solutions of a two-wave mode Korteweg-de Vrie equation

[1] A.R Adem and X. L¨u, Travelling wave solutions of a two-dimensional generalized Sawada-Kotera equation, Nonlinear Dyn. 84 (2016) 915–922.
[2] M.R. Alharthi, R.A. Alotabi, K.A. Gepreel and M.S. Mohamed, Homotopy analysis transform Method for integrodifferential equations, General Math. Notes 32 (2016) 32–48.
[3] N.S. Al-Sayali, K.A. Gepreel and T.A. Nofal, Direct method for solving nonlinear strain wave equation in microstructure solids, Int. J. Phys. Sci. 11 (2016) 121–131.
[4] N.S. Al-Sayali, K.A. Gepreel and T.A. Nofal, Exact solutions to the generalized Hirota-Satsuma KdV equations
using the extended trial equation method, Engin. Lett. 24 (2016) 274–283.
[5] K.O. Alweil, K.A. Gepreel and T.A. Nofal, Simplest equation method for nonlinear evolution equations in mathematical physics, WSEAS Trans. Math. 15 (2016) 2224–2880.
[6] S.C. Anco and G.W. Bluman, Direct construction method for conservation laws of partial differential equations.
Part I: Examples of conservation law classifications, Euro. J. Appl. Math. 13 (2002) 545–566.
[7] M. Azadi, H. Jafari and H.G. Sun, Lie symmetry reductions of coupled KdV system of fractional order, Nonlinear
Dyn. Syst. Theory 18(1) (2018) 22–28.
[8] D. Baleanu, N. Kadkhoda, H. Jafari and G.M. Moremedi, Optimal system and symmetry reduction of the (1+1)
dimensional Sawada-Kotera equation, Int. J. Pure Appl. Math. 108(2) (2016) 215–226.
[9] G.W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York, 1989.
[10] G. Carnevale, M. Tabor and J. Weiss, The Painlev´e property for partial differential equations, J. Math. Phys. 24
(1983) 522–526.
[11] S. Chen, C.M. Khalique, X. L¨u and W.X. Ma, A note on rational solutions to a Hirota-Satsuma-like equation,
Appl. Math. Lett. 58 (2016) 13–18.[12] S.T Chen, X. L¨u and W.X. Ma, Constructing lump solutions to a generalized Kadomtsev-Petviashvili-Boussinesq
equation, Nonlinear Dyn. 86 (2016) 523–534.
[13] D. Feng and K. Li, Exact traveling wave solutions for a generalized Hirota-Satsuma coupled KdV equation by Fan
sub-equation method, Phys. Lett. A 375 (2012) 2201–2210.
[14] K.A. Gepreel, Exact solutions for nonlinear integral member of Kadomtsev-Petviashvili hierarchy differential
equations using the modified (w/g)-expansion method, Comput. Math. Appl. 72 (2016) 2072–2083.
[15] K.A. Gepreel and M.S. Mohamed, Reduced differential transform method for nonlinear integral member of
Kadomtsev-Petviashvili hierarchy differential equations, J. Egyptian Math. Soc. 25 (2017) 1-–7.
[16] R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett.
27 (1971) 1192–1194.
[17] H. Jafari, M. Khorshidi, M. Nadjafikhah and M. A. Qurashi, Reductions and conservation laws for BBM and
modified BBM equations, Open Math. 14(1) (2016) 1138–1148.
[18] N. Kadkhoda and H. Jafari, Kudryshov method for solutions of isothermal magnetostatic atmospheres, Iran. J.
Numerical Anal. Optim. 6 (2016) 43–52.
[19] A.H. Kara and F.M. Mahomed, Relationship between symmetries and conservation laws, Int. J. Theo. Phys. 39
(2000) 23–40.
[20] F. Lin and X. L¨u, Soliton excitations and shape-changing collisions in alpha helical proteins with interspine
coupling at higher order, Commun. Nonlinear Sci. Numerical Simul. 32 (2016) 241–261.
[21] L. Ling and X. L¨u, Vector bright solitons associated with positive coherent coupling via Darboux transformation,
Chaos 25 (2015) 1–8.
[22] X. L¨u and W.X. Ma, Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation, Nonlinear
Dyn. 85 (2016) 1217–1222.
[23] A. Sj¨oberg, Double reduction of partial differential equations from the association of symmetries with conservation
laws with application, Appl. Math. Comput. 184 (2007) 608–616.
[24] H. Steudel, Uber die zuordnung zwischen invarianzeigenschaften und erhaltungssatzen, Z. Natur. 17A (1962)
129–132.
[25] N.K. Vitanov, On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear
PDEs: The role of the simples equation, Commun. Nonlinear Sci. Numerical Simul. 16 (2011) 4215–4231.
[26] M.L. Wang, Exact solution for a compound KdV-Burgers equations, Phys. Lett. A 213 (1996) 279–287.
[27] A.M. Wazwaz, Completely integrable coupled KdV and coupled KP systems, Commun. Nonlinear Sci. Numerical
Simul. 15 (2010) 2828–2835.
[28] A.M. Wazwaz, A two-wave mode KdV equation with multiple soliton solutions, Appl. Math. Lett. 70 (2017) 1–6.
[29] E. Yomba, The modified extended Fan sub-equation method and its application to the (2+1)-dimensional BroerKaup-Kupershmidt equation, Chaos, Solitons Fract. 27 (2006) 187–196.