Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities-Reference-Cited by-同舟云学术

Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities

Published:2018-06-28 Issue:10 Volume:73 Page:883-892
ISSN:1865-7109
Container-title:Zeitschrift für Naturforschung A
language:en
Short-container-title:

Author:

Mancas Stefan C.¹^ORCID,Rosu Haret C.²^ORCID,Pérez-Maldonado Maximino²

Affiliation:

1. Department of Mathematics, Embry-Riddle Aeronautical University , Daytona Beach, FL 32114-3900 , USA

2. 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

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/zna-2018-0055/pdf

Reference42 articles.

1. E. Bour, J. Ecole Imperiale Polytechnique 19, 1 (1862).

2. G. Tzitzéica, C.R. Acad. Sci. Paris 144, 1257 (1907).

3. G. Tzitzéica, Rend. Circ. Mat. Palermo 25, 180 (1908); ibid 28, 210 (1909).

4. G. Tzitzéica, C.R. Acad. Sci. Paris 150, 955, 1227 (1910).

5. R. K. Dodd and R. K. Bullough, Proc. R. Soc. A 352, 481 (1977).

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Liouville soliton surfaces obtained using Darboux transformations;Physica Scripta;2023-06-26

2. The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations;International Journal of Nonlinear Sciences and Numerical Simulation;2021-03-18