Dynamics of periodic soliton solutions to the AB system under vanishing boundary condition

• Published in: Nonlinear dynamics Vol. 113; no. 1; pp. 783 - 797
• Main Authors: Zhou, Fang, Mihalache, Dumitru, Zhang, Shanlin, Rao, Jiguang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2025; Springer Nature B.V
• Subjects: Amplitudes; Applications of Nonlinear Dynamics and Chaos Theory; Asymptotic methods; Boundary conditions; Classical Mechanics; Control; Dynamical Systems; Exact solutions; Nonlinear dynamics; Physics; Physics and Astronomy; Solitary waves; Statistical Physics and Dynamical Systems; Velocity; Vibration; Long-time asymptotic analysis; Bilinear method; Periodic solitons; AB system
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-10273-y

This study explores the dynamics and interaction characteristics of multiple periodic soliton solutions within the AB system subject to vanishing boundary condition (VBC). Utilizing the bilinear method associated with tau functions from the extended KP hierarchy, the exact solution family corresponding to periodic solitons under VBC in the AB system is constructed. A notable difference between the single periodic soliton in the complex component A and the real component B lies in the relationship between its velocity and its amplitude. In component A , the relationship is nonlinear, whereas in component B , its velocity is directly proportional to its amplitude. The large-time asymptotic expressions of the multiple periodic soliton solutions, given by the sum of individual single periodic solitons under VBC, are explicitly derived to reveal their collision characteristic. Our findings demonstrate the robustness and intricate interaction patterns of periodic solitons under VBC, contributing to a deeper understanding of nonlinear periodic wave dynamics in infinite domains.