About: General Solution For Generalised Newell-Whitehead-Segel Equations

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
title	General Solution For Generalised Newell-Whitehead-Segel Equations
source	ArXiv
abstract	In this monograph, two sets of parabolic differential equations are studied, each with nonlinear medium response. The equations are generally referred to as%22Newell-Whitehead-Segel equation,%22which model a wide variety of nonlinear physical, mechanical and biological systems. Nonlinear medium response can be viewed in many perspectives, such as, memory response from the medium, whereby, the medium%22remembers%22earlier influences; reactive responses, whereby, the medium is actively responsive to input, such as, chemical reactivity, turbulence and many other circumstances; these equations arise often in the biological sciences when modeling population dynamics, whether the population be genomic, such as, alleles, or animal species in the environment; finally, these sets of equations are often employed to model neurological responses from excitable cellular media. The solutions provided are of a very general nature, indeed, whereby, a canonical set of solutions are given for a class of nonlinear parabolic partial differential equations with nonlinear medium response expressed as either a p-times iterative convolution or p-times multiplicative response. The advantage of canonical solution sets are these solutions involve classic representative forms, such as, Green's function or Green's heat kernel and aid researchers in further complication, analysis and understanding of the systemic behavior of these types of nonlinear systems.
has issue date	2020-08-05(xsd:dateTime)
has license	arxiv
sha1sum (hex)	0653c16f08f1cc361293910f820ec70fa552e69a
resource representing a document's title	General Solution For Generalised Newell-Whitehead-Segel Equations
resource representing a document's body	covid:0653c16f08f1cc361293910f820ec70fa552e69a#body_text
is schema:about of	named entity 'General Solution' named entity 'spatial dependence' named entity 'Green's function' named entity 'quantum mechanics' named entity 'Green's function' »more»

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