New perspective on fractional Hamiltonian amplitude equation

• Published in: Optical and quantum electronics Vol. 55; no. 12
• Main Author: Wang, Kang-Le
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2023; Springer Nature B.V
• Subjects: Amplitudes; Characterization and Evaluation of Materials; Computer Communication Networks; Electrical Engineering; Lasers; Nonlinear dynamics; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Solitary waves; Soliton solution; Beta fractional derivative; method; Fractional rational; Fractional Hamiltonian amplitude equation
• ISSN: 0306-8919; 1572-817X
• DOI: 10.1007/s11082-023-05309-3

In this paper, we present a pioneering investigation on the fractional Hamiltonian amplitude equation involving the beta fractional derivative for the first time, addressing a research gap in the field of nonlinear fractional dynamics. Our primary objective is to develop effective analytical techniques capable of solving the fractional Hamiltonian amplitude equation and obtaining novel soliton solutions. To achieve this, we introduce two advanced methods: the extended fractional rational sin e δ - cos i n e δ and the fractional rational sinh δ - cosh δ techniques. By employing these cutting-edge approaches, we successfully derive new types of soliton solutions, demonstrating the reliability and efficiency of the proposed methods. Furthermore, the applicability of these techniques extends to various fractional nonlinear evolution models, highlighting their versatility in the realm of fractional dynamics. Finally, we provide a comprehensive presentation of the results, which substantiate the effectiveness of the methods in solving the complex fractional Hamiltonian amplitude equation.