Work

The Period Function of the Generalized Sine-Gordon Equation and the Sinh-Poisson Equation

Year: 2024

Type: article

Abstract: In this paper, we consider the generalized sine-Gordon equation ψtx=(1+a∂x2)sinψ and the sinh-Poisson equation uxx+uyy+σsinhu=0, where a is a real parameter, and σ is a positive parameter. Under different conditions, e.g., a=0, a≠0, and σ>0, the periods of the periodic wave solutions for the above two equations are discussed. By the transformation of variables, the generalized sine-Gordon equation and sinh-Poisson equations are reduced to planar dynamical systems whose first integral includes trigonometric terms and exponential terms, respectively. We successfully handle the trigonometric terms and exponential terms in the study of the monotonicity of the period function of periodic solutions.

Source: Mathematics

DOI: 10.3390/math12162474

Authors: Lin Lu, Xiaokai He, Xing Zhou

Institution: Hunan First Normal University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: Education Department of Hunan Province, National Natural Science Foundation of China, Natural Science Foundation of Hunan Province