Several classes of exact solutions to the 1+1 Born-Infeld equation

    Authors

    K. Mallory; R. A. Van Gorder;K. Vajravelu

    Comments

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    Abbreviated Journal Title

    Commun. Nonlinear Sci. Numer. Simul.

    Keywords

    Born-Infeld model; Nonlinear electrodynamics; Exact solutions; GRAVITATIONAL INSTANTONS; FIELD-THEORY; DYNAMICS; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical

    Abstract

    We obtain closed-form exact solutions to the 1 + 1 Born-Infeld equation arising in nonlinear electrodynamics. In particular, we obtain general traveling wave solutions of one wave variable, solutions of two wave variables, similarity solutions, multiplicatively separable solutions, and additively separable solutions. Then, putting the Born-Infeld model into correspondence with the minimal surface equation using a Wick rotation, we are able to construct complex helicoid solutions, transformed catenoid solutions, and complex analogues of Scherk's first and second surfaces. Some of the obtained solutions are new, whereas others are generalizations of solutions in the literature. These exact solutions demonstrate the fact that solutions to the Born-Infeld model can exhibit a variety of behaviors. Exploiting the integrability of the Born-Infeld equation, the solutions are constructed elegantly, without the need for complicated analytical algorithms. (C) 2013 Elsevier B.V. All rights reserved.

    Journal Title

    Communications in Nonlinear Science and Numerical Simulation

    Volume

    19

    Issue/Number

    6

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    1669

    Last Page

    1674

    WOS Identifier

    WOS:000328732900003

    ISSN

    1007-5704

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