New exact fronts for the nonlinear diffusion equation with quintic nonlinearities

Details New exact fronts for the nonlinear diffusion equation with quintic nonlinearities New exact fronts for the nonlinear diffusion equation with quintic nonlinearities

1994-03-21

arxiv.org/abs/patt-sol/9403003v1

Phys. Rev. E, 50 (1994) 3701

Nonlinear Sciences

Pattern Formation and Solitons

Revtex, 5 pages

Scientific paper

10.1103/PhysRevE.50.3701

We consider travelling wave solutions of the reaction diffusion equation with quintic nonlinearities $u_t = u_{xx} + \mu u (1 -u ) ( 1 +\alpha u + \beta u^2 +\gamma u^3)$. If the parameters $\alpha , \beta$ and $\gamma$ obey a special relation, then the criterion for the existence of a strong heteroclinic connection can be expressed in terms of two of these parameters. If an additional restriction is imposed, explicit front solutions can be obtained. The approach used can be extended to polynomials whose highest degree is odd.

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