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1-soliton solution of the coupled KdV equation and Gear-Grimshaw model. (English) Zbl 1197.35215
Summary: This paper carries out the integration of the coupled KdV equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. The domain restrictions of the coefficients of nonlinear and dispersion terms fall out. The results are then supplemented by numerical simulations.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35C08Soliton solutions of PDE
35C05Solutions of PDE in closed form
References:
[1]Antonova, M.; Biswas, A.: Adiabatic parameter dynamics of perturbed solitary waves, Communications in nonlinear science and numerical simulation 14, No. 3, 734-748 (2009) · Zbl 1221.35321 · doi:10.1016/j.cnsns.2007.12.004
[2]Bisognin, E.; Bisognin, V.; Sepulveda, M.; Vera, O.: Coupled system of Korteweg – de Vries equations type in domains with moving boundaries, Journal of computational and applied mathematics 220, No. 1 – 2, 290-321 (2008) · Zbl 1158.65056 · doi:10.1016/j.cam.2007.08.008
[3]Kudryashov, N. A.; Loguinova, N. B.: Seven common errors in finding exact solutions of nonlinear differential equations, Communications in nonlinear science and numerical simulation 14, No. 9 – 10, 3507-3529 (2009) · Zbl 1221.35342 · doi:10.1016/j.cnsns.2009.01.023
[4]Kivshar, Y. S.; Malomed, B. A.: Solitons in a system of coupled Korteweg – de Vries equations, Wave motion 11, No. 3, 261-269 (1989) · Zbl 0692.76012 · doi:10.1016/0165-2125(89)90005-X
[5]Kivshar, Y.; Malomed, B. A.: Dynamics of solitons in nearly integrable systems, Reviews of modern physics 61, No. 4, 763-915 (1989)
[6]Xiao-Yan, T.; Fei, H.; Sen-Yue, L.: Variable coefficient KdV equation and the analytical diagnosis of a dipole blocking life cycle, Chinese physics letters 23, 887-890 (2006)
[7]H. Triki, M.S. Ismail, Solitary wave solutions for a coupled pair of mKdV equations, Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2009.06.047.
[8]Wazwaz, A. M.: The extended tanh method for new solitons for many forms of the fifth-order KdV equations, Applied mathematics and computation 184, No. 2, 1002-1014 (2007) · Zbl 1115.65106 · doi:10.1016/j.amc.2006.07.002
[9]Wazzan, L.: A modified tanh – coth method for solving KdV and the KdV – burger’s equation, Communications in nonlinear science and numerical simulation 14, No. 2, 443-450 (2009) · Zbl 1221.35376 · doi:10.1016/j.cnsns.2007.06.011
[10]Zhang, H.: New exact solutions for two generalized Hirota – satsuma coupled KdV systems, Communications in nonlinear science and numerical simulation 12, No. 7, 1120-1127 (2009)