Work

A Study of a (3+1)-Dimensional Hirota Bilinear Model with Variable Coefficients: Generalized Higher-Order Rogue Waves and Wronskian Solutions

Year: 2025

Type: article

Abstract: The Hirota bilinear equation with variable coefficients (VCs) serves as a fundamental model for capturing nonlinear wave dynamics in fluids and oceans. Utilizing the Hirota bilinear framework alongside advanced symbolic computation techniques, higher-order rational solutions to this equation have been comprehensively investigated. These solutions unveil a wide range of waveforms, including multi-rogue waves (RWs) and multi-parallel solitons. To further expand the solution space, the rational solutions have been generalized by introducing two adjustable parameters, $$\alpha $$ α and $$\beta $$ β , referred to as center control parameters. These parameters enable the generation of a versatile class of nonlinear, controllable RWs, enhancing the flexibility and applicability of the model. Soliton solutions have also been constructed using the Wronskian method, with their validity rigorously established through proofs grounded in Plücker relations. By employing various functional forms for the VCs, the dynamic properties of these solutions have been extensively analyzed and visualized through three-dimensional representations, showcasing their rich complexity and diverse behaviors.

Source: Qualitative Theory of Dynamical Systems

DOI: 10.1007/s12346-025-01292-0

Author: Majid Madadi

Institution: Institute for Advanced Studies in Basic Sciences

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funder: Firat Üniversitesi