Title
Several Classes Of Exact Solutions To The 1+1 Born-Infeld Equation
Keywords
Born-Infeld model; Exact solutions; Nonlinear electrodynamics
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. © 2013 Elsevier B.V.
Publication Date
6-1-2014
Publication Title
Communications in Nonlinear Science and Numerical Simulation
Volume
19
Issue
6
Number of Pages
1669-1674
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.cnsns.2013.09.034
Copyright Status
Unknown
Socpus ID
84890786544 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84890786544
STARS Citation
Mallory, Kristina; Van Gorder, Robert A.; and Vajravelu, Kuppalapalle, "Several Classes Of Exact Solutions To The 1+1 Born-Infeld Equation" (2014). Scopus Export 2010-2014. 8539.
https://stars.library.ucf.edu/scopus2010/8539