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| Content Provider | Springer Nature Link |
|---|---|
| Author | Bradshaw Hajek, B. H. Broadbridge, P. |
| Copyright Year | 2016 |
| Abstract | Reaction–diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms. |
| Ending Page | 13 |
| Page Count | 13 |
| Starting Page | 1 |
| File Format | |
| ISSN | 00442275 |
| e-ISSN | 14209039 |
| Journal | Zeitschrift für angewandte Mathematik und Physik |
| Issue Number | 4 |
| Volume Number | 67 |
| Language | English |
| Publisher | Springer International Publishing |
| Publisher Date | 2016-07-16 |
| Publisher Place | Cham |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Population dynamics (general) Reaction–diffusion equations Fisher equation Mathematical Methods in Physics Exact solutions Reaction-diffusion equations Theoretical and Applied Mechanics Fitzhugh–Nagumo equation KPP equation Nonclassical symmetries Nonlinear parabolic equations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Physics and Astronomy |
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