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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus


IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

Online
ISSN
1865-7109
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Volume 73, Issue 10

Issues

Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities

Stefan C. MancasORCID iD: https://orcid.org/0000-0003-1175-6869 / Haret C. RosuORCID iD: https://orcid.org/0000-0001-5909-1945 / Maximino Pérez-Maldonado
  • IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potos, S.L.P., Mexico
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Published Online: 2018-06-28 | DOI: https://doi.org/10.1515/zna-2018-0055

Abstract

We use a simple method that leads to the integrals involved in obtaining the travelling-wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in terms of hypergeometric functions are obtained, while when that term is nonzero, all the basic travelling-wave solutions of Liouville, Tzitzéica, and their variants, as as well sine/sinh-Gordon equations with important applications in the phenomenology of nonlinear physics and dynamical systems are found through a detailed study of the corresponding elliptic equations.

Keywords: Dodd-Bullough; Dodd-Bullough-Mikhailov; Liouville Equation; sine-Gordon; sinh-Gordon; Tzitzéica; Weierstrass Function

PACS: 02.30.Hq; 04.20.Jb; 02.30.Ik

References

About the article

Received: 2018-02-01

Accepted: 2018-06-04

Published Online: 2018-06-28

Published in Print: 2018-10-25


Citation Information: Zeitschrift für Naturforschung A, Volume 73, Issue 10, Pages 883–892, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2018-0055.

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