Title

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

Authors

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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