### Abstract

A class of nonlinear equations describing the steady propagation of a disturbance on the infinite interval in one dimensional space are shown under certain conditions to admit solution with a unique velocity of propagation. The class of equations describe both initial and final homogeneous steady states which are asymptotically stable with respect to uniform perturbations, in contrast to the Fisher equation, which does not.

Original language | English |
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Pages (from-to) | 321-337 |

Number of pages | 17 |

Journal | Bulletin of Mathematical Biology |

Volume | 44 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 1982 |

### Keywords

- flame front
- nonlinear wave equation
- laminar flame
- intersection theorem
- initial singularity

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## Cite this

Gray, B. F., & Sherrington, M. E. (1982). Eigensolutions of nonlinear wave equations in one dimension.

*Bulletin of Mathematical Biology*,*44*(3), 321-337. https://doi.org/10.1007/BF02462283