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The investigation into the exact solutions of the generalized time-delayed Burgers-Fisher equation with positive fractional power terms. (English) Zbl 1242.35197
Summary: The time-delayed Burgers-Fisher equation is very important model to forest fire, population growth, Neolithic transitions, the interaction between the reaction mechanism, convection effect and diffusion transport, etc. In this paper, the solitary wave solutions of the generalized time-delayed Burgers-Fisher equation with positive fractional power terms are derived with the aid of a subsidiary high-order ODE, and the solitary wave solutions of the special type of generalized time-delayed Burgers-Fisher equation are presented. From the expressions of the solitary wave solutions, it is easy to obtain how the time-delayed constant τ works upon soliton velocity and width of the soliton, and these exact solutions are very important to understand the physical mechanism of the phenomena described by the time-delayed Burgers-Fisher equation.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35L72Quasilinear second-order hyperbolic equations
35C07Traveling wave solutions of PDE
References:
[1]Kolmanovskii, V. B.; Myshkis, A.: Introduction to the theory and applications of functional differential equations, (1999)
[2]Niculescu, S. I.: Delay effects on stability, Lecture notes in control and information sciences 269 (2001)
[3]Hale, J. K.; Lunel, S. M. V.: Introduction to functional differential equations, Applied mathematical sciences 99 (1993) · Zbl 0787.34002
[4]Rendine, S.; Piazza, A.; Cavalli-Sforza, L. L.: Simulation and separation by principle components of multiple demic expansions in Europe, Am. nat. 128, 681-706 (1986)
[5]Ammerman, A. J.; Cavalli-Sforza, L. L.: The neolithic transition and the genetics of population in Europe, (1984)
[6]Galenko, P. K.; Danilov, D. A.: Selection of the dynamically stable regime of rapid solidification front motion in an isothermal binary alloy, J. cryst. Growth 216, 512-536 (2000)
[7]Fahmy, E. S.: Travelling wave solutions for some time-delayed equations through factorizations, Chaos solitons fract. 38, 1209-1216 (2008) · Zbl 1152.35438 · doi:10.1016/j.chaos.2007.02.007
[8]Wang, X. Y.; Lu, Y. K.: Exact solutions of the extended Burgers – Fisher equation, Chinese phys. Lett. 7, 145-147 (1990)
[9]Deng, X. J.; Han, L. B.; Li, X.: Travelling solitary wave solutions for generalized time-delayed Burgers – Fisher equation, Commun. theor. Phys. 52, 284-286 (2009) · Zbl 1183.35233 · doi:10.1088/0253-6102/52/2/19
[10]Abdusalam, H. A.; Fahmy, E. S.: Exact solution for the generalized telegraph Fisher’s equation chaos, Solitons fract. 41, 1550-1556 (2009) · Zbl 1198.35139 · doi:10.1016/j.chaos.2008.06.018
[11]Hyunsoo Kim, Rathinasamy Sakthivel, Travelling wave solutions for time-delayed nonlinear evolution equations, Appl. Math. Lett. doi:10.1016/j.aml.2010.01.005.
[12]Anwar Ja’afar Mohamad Jawad, Marko D. Petkovic ' , Anjan Biswas, Soliton solutions of Burgers equations and perturbed Burgers equation, Appl. Math. Comput. 216 (2010) 3370 – 3377. · Zbl 1195.35262 · doi:10.1016/j.amc.2010.04.066
[13]Fahmy, E. S.; Abdusalam, H. A.; Raslan, K. R.: On the solutions of the time-delayed Burgers equation, Nonlinear anal. 69, 4775-4786 (2008) · Zbl 1165.35304 · doi:10.1016/j.na.2007.11.027
[14]Wang, M. L.: Solitary wave solutions for variant Boussinesq equations, Phys. lett. A 199, 169-172 (1995) · Zbl 1020.35528 · doi:10.1016/0375-9601(95)00092-H
[15]Wang, M. L.: Exact solutions of a compound KdV-Burgers equation, Phys. lett. A 213, 279-287 (1996) · Zbl 0972.35526 · doi:10.1016/0375-9601(96)00103-X
[16]Zhang, J. L.; Wang, Y. M.; Wang, M. L.; Fang, Z. -D.: New application of the homogeneous balance principle, Chinese phys. 12, 245-250 (2003)
[17]Wang, M. L.; Wang, Y. M.: A new Bäcklund transformation and multi-solutions to the KdV equation with general variable coefficients, Phys. lett. A 287, 211-216 (2001) · Zbl 0971.35064 · doi:10.1016/S0375-9601(01)00487-X