Traveling Waves for the Generalized Sinh-Gordon Equation with Variable Coefficients

Lewa’ Alzaleq, Du’a Al-zaleq and Suboh Alkhushayni
Additional contact information
Lewa’ Alzaleq: Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan
Du’a Al-zaleq: Computer Information Science Department, Minnesota State University, Mankato, MN 56001, USA
Suboh Alkhushayni: Computer Information Science Department, Minnesota State University, Mankato, MN 56001, USA

Mathematics, 2022, vol. 10, issue 5, 1-11

Abstract: The sinh-Gordon equation is simply the classical wave equation with a nonlinear sinh source term. It arises in diverse scientific applications including differential geometry theory, integrable quantum field theory, fluid dynamics, kink dynamics, and statistical mechanics. It can be used to describe generic properties of string dynamics for strings and multi-strings in constant curvature space. In the present paper, we study a generalized sinh-Gordon equation with variable coefficients with the goal of obtaining analytical traveling wave solutions. Our results show that the traveling waves of the variable coefficient sinh-Gordon equation can be derived from the known solutions of the standard sinh-Gordon equation under a specific selection of a choice of the variable coefficients. These solutions include some real single and multi-solitons, periodic waves, breaking kink waves, singular waves, periodic singular waves, and compactons. These solutions might be valuable when scientists model some real-life phenomena using the sinh-Gordon equation where the balance between dispersion and nonlinearity is perturbed.

Keywords: sinh-Gordon equation; space and time dependent coefficients; soliton; periodic waves; traveling wave solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/5/822/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/5/822/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:5:p:822-:d:764166

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().