Work

Elliptic Functions and Advanced Analysis of Soliton Solutions for the Dullin–Gottwald–Holm Dynamical Equation with Applications of Mathematical Methods

Year: 2025

Type: article

Abstract: We studied traveling-wave solutions of the Dullin–Gottwald–Holm (DGH) equation via a sub-ODE construction. Under explicit algebraic constraints, the approach yielded closed-form families—bell-shaped, hyperbolic (sech/tanh), Jacobi-elliptic function (JEF), Weierstrass-elliptic function (WEF), periodic, and rational—and classified their symmetry properties. Optical solitons (bright and dark) arose as limiting cases of the elliptic solutions. We specified the parameter regimes that produced each profile and illustrated representative solutions with 2D/3D plots to highlight symmetry. The results provide a unified, reproducible procedure for generating solitary and periodic DGH waves and expand the catalog of exact solutions for this model.

Source: Symmetry

DOI: 10.3390/sym17101773

Authors: Syed T. R. Rizvi, Ibtehal Alazman, Nimra, Aly R. Seadawy

Institutions: COMSATS University Islamabad, Imam Mohammad ibn Saud Islamic University, Taibah 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: $2,896

Funder: Al-Imam Muhammad Ibn Saud Islamic University