A Linearization Approach for Rational Nonlinear Models in Mathematical Physics

    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