Eigensolutions of nonlinear wave equations in one dimension

B. F. Gray*, M. E. Sherrington

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)321-337
Number of pages17
JournalBulletin of Mathematical Biology
Issue number3
Publication statusPublished - May 1982


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


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