کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6422042 | 1340607 | 2011 | 14 صفحه PDF | دانلود رایگان |
Based on the simplest equation method, we propose exact and traveling-wave solutions for a nonlinear convection-diffusion-reaction equation with power law nonlinearity. Such equation can be considered as a generalization of the Fisher equation and other well-known convection-diffusion-reaction equations. Two important cases are considered. The case of density-independent diffusion and the case of density-dependent diffusion. When the parameters of the equation are constant, the Bernoulli equation is used as the simplest equation. This leads to new traveling-wave solutions. Moreover, some wavefront solutions can be derived from the traveling-wave ones. The case of time-dependent velocity in the convection term is studied also. We derive exact solutions of the equations by using the Riccati equation as simplest equation. The exact and traveling-wave solutions presented in this paper can be used to explain many biological and physical phenomena.
Journal: Applied Mathematics and Computation - Volume 218, Issue 6, 15 November 2011, Pages 2407-2420