dorsal/arxiv
View SchemaNew exact fronts for the nonlinear diffusion equation with quintic nonlinearities
| Authors | R. D. Benguria, M. C. Depassier |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9403003 |
| URL | https://arxiv.org/abs/patt-sol/9403003 |
| DOI | 10.1103/PhysRevE.50.3701 |
| Journal | Phys. Rev. E, 50 (1994) 3701 |
Abstract
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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"abstract": "We consider travelling wave solutions of the reaction diffusion equation with\nquintic nonlinearities $u_t = u_{xx} + \\mu u (1 -u )\n ( 1 +\\alpha u + \\beta u^2 +\\gamma u^3)$. If the parameters $\\alpha , \\beta$\nand $\\gamma$ obey a special relation, then the criterion for the existence of a\nstrong heteroclinic connection can be expressed in terms of two of these\nparameters. If an additional restriction is imposed, explicit front solutions\ncan be obtained. The approach used can be extended to polynomials whose highest\ndegree is odd.",
"arxiv_id": "patt-sol/9403003",
"authors": [
"R. D. Benguria",
"M. C. Depassier"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.50.3701",
"journal_ref": "Phys. Rev. E, 50 (1994) 3701",
"title": "New exact fronts for the nonlinear diffusion equation with quintic nonlinearities",
"url": "https://arxiv.org/abs/patt-sol/9403003"
},
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