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Soliton solutions of Burgers equations and perturbed Burgers equation. (English) Zbl 1195.35262
Summary: This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV-Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in $\left(1+1\right)$ dimensions is integrated by the ansatz method.
##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35A30 Geometric theory for PDE, characteristics, transformations 35C08 Soliton solutions of PDE 35A24 Methods of ordinary differential equations for PDE
##### Keywords:
solitons; exact solutions; tanh method
##### References:
 [1] Abdou, M. A.; Soliman, A. A.: Variational iteration method for solving Burgers and coupled Burgers equations, Journal of computational and applied mathematics 181, No. 2, 245-251 (2005) · Zbl 1072.65127 · doi:10.1016/j.cam.2004.11.032 [2] Abdusalam, H. A.: Exact analytic solution of the simplified telegraph model of propagation and dissipation of exciton fonts, International journal of theoretical physics 43, No. 4, 1161-1167 (2004) · Zbl 1175.92010 · doi:10.1023/B:IJTP.0000048607.06704.8d [3] Bahadir, A. R.: A fully implicit finite difference scheme for two dimensional Burgers equation, Applied mathematics & computation 137, 131-137 (2003) [4] Kar, S.; Banik, S. K.; Ray, D. S.: Exact solutions of Fisher and Burgers equations with finite transport memory, Journal of physics A 36, 2771-2780 (2003) · Zbl 1039.35067 · doi:10.1088/0305-4470/36/11/308 [5] Kraenkel, R. A.; Pereira, J. G.; De Rey Neto, E. C.: Linearizability of the perturbed Burgers equation, Physical review E 58, No. 2, 2526 (1998) [6] Majid, F. B.; Ranasinghe, A. I.: Solution of the Burgers equation using an implicit linearizing scheme, Communications in nonlinear science and numerical simulation 14, No. 5, 1861-1867 (2009) · Zbl 1221.35354 · doi:10.1016/j.cnsns.2008.09.012 [7] Nee, J.; Duan, J.: Limit set trajectories of the coupled viscous Burgers equations, Applied mathematics letters 11, No. 1, 57-61 (1998) · Zbl 1076.35537 · doi:10.1016/S0893-9659(97)00133-X [8] Wazwaz, A. -M.: Multiple kink solutions and multiple singular kink solutions for the (2+1) dimensional Burgers equations, Applied mathematics & computation 204, No. 2, 817-823 (2008) [9] Wazwaz, A. -M.: Multiple kink solutions and multiple singular soliton solutions for the (3+1) dimensional Burgers equations, Applied mathematics & computation 204, No. 2, 942-948 (2008) [10] Wazwaz, A. -M.: Burgers hierarchy: multiple kink solutions and multiple singular kink solutions, Journal of the franklin institute 347, No. 3, 618-626 (2010) · Zbl 1225.35191