Exact and traveling-wave solutions for convection-diffusion-reaction equation with power-law nonlinearity |
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Authors: | Mohamed Hayek |
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Institution: | Paul Scherrer Institut, Laboratory for Waste Management, CH-5232 Villigen PSI, Switzerland |
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Abstract: | 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. |
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Keywords: | Nonlinear convection-diffusion-reaction equation Power-law nonlinearity Traveling-wave solutions Wavefront solutions Exact solutions Simplest equation method |
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