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Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation


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Kraenkel R. A.,Es1 := 0;blondand H L. and Manna M A An integrable evolution equation for surface waves in deep water., J. Phys. A: Math. Theor. 47 (2014) 025208-145208. Search in Google Scholar

Abdel-Gawad H. I.,Towards a unified method for exact solutions of evolution equations. An application to reaction diffusion equations with finite memory transport. J Stat.l Phys. 147 (2012), 506-518. Search in Google Scholar

Abdel-Gawad, H. I., El-Azab N., and Osman M., Exact solution of the space-dependent KdV equation by the extended unified method, JPSP, 82 (2013) 044004,. Search in Google Scholar

Abdel-Gawad H. I., On the “ˆkp-operator”, new extension of the KdV6 to (m+1)-dimensional equation and traveling waves solutions, Nonlinear Dyn.., 85 (2016 ) 1509–1515. Search in Google Scholar

Abdel-Gawad H. I., and Osman M. S., “Exact solutions of the Korteweg-de Vries equation with space and time dependent coefficients by the extended unified method. Indian j. pure nd Appl. Math., vol. 45 (2014) 1-12. Search in Google Scholar

Constantin, A., Escher, J., Symmetry of steady deep-water waves with vorticity. Eur. J. of Appl. Math. 15 (2004), Nr. 6, S. 755-768. Search in Google Scholar

Hirota, R., Satsuma, J.:A variety of nonlinear network equations generated from the B”«klund transformation for the Toda lattice. Suppl. Prog. Theor. 59 (1976)64–100. Search in Google Scholar

Mikhailov A. V.,The reduction problem and the inverse scattering method, Physica D, Volume 3,( 1981) 73-117. Search in Google Scholar

Sayed S. M., The B”«klund Transformations, Exact Solutions, and Conservation Laws for the Compound Modified Korteweg-de Vries-Sine-Gordon Equations which Describe Pseudospherical Surfaces 2013(2013)ID 613065, 7p. Search in Google Scholar

Bluman, G.W., Kumei, S.: Symmetries and Differential Equations. Springer, Berlin (1989). Search in Google Scholar

Guo, X., Lu, L., Mo, D.: Traveling wave solutions of an integrable evolution equation for surface waves. Far East J. Math. Sci. 93 (2014) 175–184 . [1] Yang, H., Liu, W., Yang, B., He, B.: Lie symmetry analysis and exact explicit solutions of three dimensional Kudryashov–Sinelshchikov equation. Nonlinear Sci. Numer. Simulat. 27 (2015) 271–280. Search in Google Scholar

Liu, Z., Guo, B.: Periodic blow-up solutions and their limit forms for the generalized Camassa–Holm equation. Prog. Nat. Sci. 18 (2008) 259–266. Search in Google Scholar

Zhang, S., Zhang, H.: An Exp-function method for new N-soliton solutions with arbitrary functions of a (2 + 1)- dimensional vcBK system. Comput.Math. Appl. 61, (2011) 1923–1930. Search in Google Scholar

Cantwell, B.J.: Introduction to Symmetry Analysis. Cambridge University Press, New York (2002). Search in Google Scholar

Olivier Kimmoun., Instabilities of steep short-crested surface waves in deep water., Phys. of Fluids (1999) 11, 1679. Search in Google Scholar

Ankiewicz A., Akhmediev N. .D.N.,Are rogue waves robust against perturbations?, Phys. Lett. A 373 (2009) 3997-4000. Search in Google Scholar

Jie H., Jingjing W., Xiumei, L., Beibei L., Wei L., Ming G., Yongwei X., Zonghang C., and Jichao M..Investigation on SurfaceWave Characteristic ofWater Jet.Mathematical Problems in Engineering 2019 (2019), Article ID 4047956, 10p. Search in Google Scholar

Abdou, M.A.: Further improved F-expansion and new exact solutions for nonlinear evolution equations. Nonlinear Dyn. 52 (2008) 277–288. Search in Google Scholar

Li,W.,Tian,Y., Zhang, Z., F-expansion method and its application for finding new exact solutions to the sine-Gordon and sinh-Gordon equations. Appl. Math. Comput. 219 (2012)1135–1143. Search in Google Scholar

Meng Q., He B., Liu W., Exact similarity and traveling wave solutions to an integrable evolution equation for surface waves in deep water., Nonlinear Dyn 92: (2018) 827–842. Search in Google Scholar

Osborne. A. R.., OnoratoMand Serio M.The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains.,Physics Letters A 275 2000. 386–393. Search in Google Scholar

Sajjadi, S. G., Mancas, S. C., & Drullion, F. Formation of Three-Dimensional Surface Waves on Deep-Water Using Elliptic Solutions of Nonlinear Schrödinger Equation. Advances and Applications in Fluid Dynamics, 18 (2015)..10.17654. Search in Google Scholar

Abdel-Gawad H. I., Waves in deep water based on based on the nonlinear Schrodinger equations with variable coefficients., Can J. Phys.92 (2014) 1-8. Search in Google Scholar

Dyachenko, A. I., & Zakharov, V. E. . A dynamic equation for water waves in one horizontal dimension. European Journal of Mechanics, B/Fluids, 32 (2012) 17-21. Search in Google Scholar

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