Nonlinear Wave Dynamics: Theory and Application

Dear Colleagues,

Since the groundbreaking work on nonlinear wave dynamics, particularly the discovery of solitons by John Scott Russell in 1834 and the subsequent mathematical formalization by Korteweg and de Vries in 1895, there has been continuous expansion in both the theoretical advancements and practical applications of nonlinear wave theory. Nonlinear waves, often governed by nonlinear partial differential equations, play a crucial role in describing a wide range of physical phenomena, such as fluid dynamics, nonlinear optics, plasma physics, and condensed matter systems. They are not only mathematically fascinating but also have significant implications for understanding complex natural systems and engineering applications.

Nonlinear waves are a complex and fascinating aspect of fluid mechanics, with profound implications for the study of ocean waves. The interplay between nonlinearity, dispersion, and external forces leads to a rich variety of wave phenomena. The study of integrable systems has spurred the development of powerful analytical methods, including the inverse scattering transform, Riemann–Hilbert problem, Hirota bilinear method, Darboux transformation, algebraic geometry techniques, and Lie symmetry analysis. These methods enable researchers to obtain exact solutions and explore the intricate behavior of nonlinear waves.

This Special Issue provides a platform for researchers from academia and industry to present their novel and unpublished works in the domain of nonlinear wave dynamics, focusing on both theoretical developments and practical applications. By highlighting advancements in the understanding of integrable systems, ocean waves, fluid mechanics, and the physical mechanisms of nonlinear waves, this Issue aims to foster future research in this interdisciplinary field, bridging the gap between mathematical theory and real-world applications.

We look forward to receiving your contributions.

Prof. Dr. Zhen Wang
Prof. Dr. Dengshan Wang
Guest Editors

Dr. Xiangyu Yang
Guest Editor Assistant

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• integrable system
• nonlinear wave
• soliton
• rogue wave
• Riemann–Hilbert problem
• inverse scattering method
• Darboux transformation
• Hirota bilinear method
• ocean wave
• fluid mechanics