On the general traveling wave solutions of some nonlinear diffusion equations

5th International Conference on "Problems of Mathematical and Theoretical Physics and Mathematical Modelling"

物理学;数学

Sinelshchikov, D.I.^1 ; Kudryashov, N.A.^1

National Research Nuclear University, MEPhl (Moscow Engineering Physics Institute), Moscow, Russia^1

关键词: Dependent variables;    General analytical solution;    Integrability;    Nonlinear diffusion equations;    Nonlinear source;    Traveling wave reductions;    Traveling wave solution;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/788/1/012033/pdf
DOI  :  10.1088/1742-6596/788/1/012033

来源: IOP

【 摘 要 】

We consider a family of nonlinear diffusion equations with nonlinear sources. We assume that all nonlinearities are polynomials with respect to a dependent variable. The traveling wave reduction of this family of equations is an equation of the Lienard-type. Applying recently obtained criteria for integrability of Lienard-type equations we find some new integrable families of traveling wave reductions of nonlinear diffusion equations as well as their general analytical solutions.