Nonlinear equations in diffusion theory
type: Item
instance of: scholarly article
title: Nonlinear equations in diffusion theory
zbMATH Open document ID: 1082.35131
DOI: 10.1023/A:1026178103584
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-06-23T00:00:00Z
review text: The paper is devoted to the study of some connections between nonlinear differential equations in diffusion theory. As is known, the Cole-Hopf substitution reduces the Burgers equation to a linear differential equation. Another example is known as the inverse scattering problem, which is based on a connection between the KdV and a linear Schrödinger equation. The connection between some nonlinear equations of soliton theory and absolute continuous transformation of diffusion measures is studied. In particular, using a multidimensional extension of the KdV equation the existence of the logarithmic derivative of a one-dimensional family of smooth measures generated by a diffusion process, is established. Also, some other connections between nonlinear equations of soliton theory and diffusion processes are studied.
reviewed by: Sabir Umarov
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J57
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 2182724
zbMATH Keywords: diffusion process
zbMATH Keywords: KdV equation
zbMATH Keywords: diffusion measure
zbMATH Keywords: Kadomtzev-Petviashvili equation
zbMATH Keywords: Schwartz equation
author: Yana Belopolskaya
MaRDI profile type: Publication
full work available at URL: a:1026178103584
OpenAlex ID: W24770455
description: scientific article; zbMATH DE number 2182724