Coherent structures of the phi(4) equation via invariant Painleve analysis

    Authors

    S. R. Choudhury;U. Tanriver

    Comments

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    Abbreviated Journal Title

    Indian J. Pure Appl. Math.

    Keywords

    coherent structures; Painleve analysis; accessibility from initial; conditions; GINZBURG-LANDAU EQUATION; EVOLUTION-EQUATIONS; MARGINAL STABILITY; PERIODIC SOLUTIONS; FRONT PROPAGATION; UNSTABLE STATES; SELECTION; EXPANSIONS; PATTERNS; PULSES; Mathematics

    Abstract

    Exact closed-form coherent structures (pulses/fronts/domain walls) having the form of complicated traveling waves are constructed via invariant Painleve analysis for the Phi(4) equation, which belongs to the family of Klein-Gordon equations. These analytical solutions, which are derived directly from the underlying PDE's, are investigated in the light of restrictions imposed by the ODE that any traveling wave reduction of corresponding PDE must satisfy. In particular, it is shown that the coherent structures a) asymptoticaly satisfy the ODE governing traveling wave reductions, and b) are accessible to the PDE from compact support initial conditions. The solutions are compared with each other, and with previously known solutions of the equation.

    Journal Title

    Indian Journal of Pure & Applied Mathematics

    Volume

    33

    Issue/Number

    4

    Publication Date

    1-1-2002

    Document Type

    Article

    Language

    English

    First Page

    495

    Last Page

    508

    WOS Identifier

    WOS:000175573700006

    ISSN

    0019-5588

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