Invariant Painleve analysis and coherent structures of long-wave equations

    Authors

    S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    Phys. Scr.

    Keywords

    GINZBURG-LANDAU EQUATION; EVOLUTION-EQUATIONS; INVERSE SCATTERING; MARGINAL STABILITY; PERIODIC SOLUTIONS; FRONT PROPAGATION; UNSTABLE; STATES; SELECTION; SYSTEMS; EXPANSIONS; Physics, Multidisciplinary

    Abstract

    Exact closed-form coherent structures (pulses/fronts/domain walls) having the form of complicated traveling waves are constructed for the long-wave (Benjamin-Bona-Mahoney/Modified-Benjamin-Bona-Mahoney/Symmetric Regularized-Long-Wave) equations by the use of invariant Painleve analysis. 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 the corresponding ODE must satisfy In particular: it is shown that the coherent structures (a) asymptotically satisfy the ODE governing traveling wave reductions, and (b) are accessible to the PDE from compact support initial conditions. The coherent structures are compared with each other, and with other known solutions of these equations.

    Journal Title

    Physica Scripta

    Volume

    62

    Issue/Number

    2-3

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    156

    Last Page

    163

    WOS Identifier

    WOS:000088902900012

    ISSN

    0281-1847

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