Abstract
A nonlinear integro-differential equation describing a diffusion process with non-local mutual interaction is considered. It can be exactly linearized by a dependent variable transformation. A perturbational approach is employed to understand the structure of solutions of the equation. First, a series of differential equations approximating the integro-differential equation is derived. Then the effect of higher order corrections on the equilibrium solution is investigated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.M.Burgers: Adv. Appl. Mech. 1, 171 (1948)
J.Satsuma: J. Phys. Soc. Jpn. 50, 1423 (1981)
T.Kawahara and M.Tanaka: Phys. Lett. 97A, 311 (1983)
K.Nozaki and N.Bekki: J. Phys. Soc. Jpn. 53, 1581 (1984)
J.Satsuma and M.Mimura: preprint, “Exact Treatment of Nonlinear Diffusion Equations with Singular Integral Terms”
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Satsuma, J. (1985). On an Exactly Solvable Nonlinear Diffusion Equation. In: Takeno, S. (eds) Dynamical Problems in Soliton Systems. Springer Series in Synergetics, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02449-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-662-02449-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02451-5
Online ISBN: 978-3-662-02449-2
eBook Packages: Springer Book Archive