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Similarity solutions of the one-dimensional Fokker-Planck equation

TitleSimilarity solutions of the one-dimensional Fokker-Planck equation
Publication TypeArticolo su Rivista peer-reviewed
Year of Publication1986
AuthorsSucci, S., and Iacono Roberto
JournalPhysical Review A
Volume33
Pagination4419-4422
ISSN10502947
Abstract

A general method recently developed to establish the conditions for the existence of similarity solutions of the Fokker-Planck-Smoluchowsky equation is applied to the one-dimensional equation P/t=(/x)[R(x)P +D(x)(P/x)]. The case of power-law behavior of the coefficient functions R(x) and D(x) is investigated in detail, and a few classes of similarity solutions are presented. In addition, a class of functions R(x) and D(x) is identified such that the general method, based on the invariance under a continuous group of transformations, is equivalent to a generalized scale transformation of the space and time variables. © 1986 The American Physical Society.

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URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-0038108985&doi=10.1103%2fPhysRevA.33.4419&partnerID=40&md5=b29530c2b8bd4e08d34deda3bd72e155
DOI10.1103/PhysRevA.33.4419
Citation KeySucci19864419