Eigensolutions of nonlinear wave equations in one dimension

B. F. Gray; M. E. Sherrington

doi:10.1007/BF02462283

Eigensolutions of nonlinear wave equations in one dimension

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	321-337
Number of pages	17
Journal	Bulletin of Mathematical Biology
Volume	44
Issue number	3
DOIs	https://doi.org/10.1007/BF02462283
Publication status	Published - May 1982

Keywords

flame front
nonlinear wave equation
laminar flame
intersection theorem
initial singularity

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title = "Eigensolutions of nonlinear wave equations in one dimension",

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.",

keywords = "flame front, nonlinear wave equation, laminar flame, intersection theorem, initial singularity",

author = "Gray, {B. F.} and Sherrington, {M. E.}",

year = "1982",

month = may,

doi = "10.1007/BF02462283",

language = "English",

volume = "44",

pages = "321--337",

journal = "Bulletin of Mathematical Biology",

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T1 - Eigensolutions of nonlinear wave equations in one dimension

AU - Gray, B. F.

AU - Sherrington, M. E.

PY - 1982/5

Y1 - 1982/5

N2 - 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.

AB - 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.

KW - flame front

KW - nonlinear wave equation

KW - laminar flame

KW - intersection theorem

KW - initial singularity

UR - http://www.scopus.com/inward/record.url?scp=49049131580&partnerID=8YFLogxK

U2 - 10.1007/BF02462283

DO - 10.1007/BF02462283

M3 - Article

AN - SCOPUS:49049131580

VL - 44

SP - 321

EP - 337

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 3

ER -

Eigensolutions of nonlinear wave equations in one dimension

Abstract

Keywords

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