Title

A Linearization Approach for Rational Nonlinear Models in Mathematical Physics

Authors

Authors

R. A. Van Gorder

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Commun. Theor. Phys.

Keywords

perturbation method; Painleve equations; delta-expansion; nonlinear; differential equations; LANE-EMDEN EQUATION; DIFFERENTIAL-EQUATIONS; PAINLEVE EQUATIONS; PERTURBATIVE APPROACH; 2ND KIND; TRANSCENDENT; POINTS; ORDER; Physics, Multidisciplinary

Abstract

In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the delta expansion method (created to deal with problems in Quantum Field Theory) which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painleve equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.

Journal Title

Communications in Theoretical Physics

Volume

57

Issue/Number

4

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

530

Last Page

540

WOS Identifier

WOS:000303049000003

ISSN

0253-6102

Share

COinS