Manuscript Topics

Nonlinear wave phenomena are central to mathematical modeling in fields such as fluid dynamics, nonlinear optics, geophysics, and plasma physics. Partial differential equations (PDEs) provide the foundational framework for describing the propagation, interaction, and evolution of waves in these complex systems. This special issue presents a curated collection of research contributions that explore the interplay between nonlinear wave behavior and emerging methodologies in PDE theory.

The assembled papers span a broad spectrum of applied mathematics, with emphasis on the formulation, analysis, and computational treatment of nonlinear and fractional PDEs governing wave dynamics. Featured topics include solitary waves, rogue wave phenomena, and dispersive shock structures, alongside advances in perturbation theory, symmetry analysis, and techniques for deriving exact and approximate solutions to nonlinear evolution equations.

A distinguishing feature of this collection is its attention to modern computational approaches, including neural network-based methods such as physics-informed neural networks (PINNs). These tools expand the range of problems accessible to PDE solvers, offering new capabilities in data-scarce environments and complex geometries.

This special issue reflects the ongoing evolution of nonlinear wave theory through the synthesis of classical analytical methods and state-of-the-art computational tools. We anticipate it will serve as a valuable resource for researchers working in nonlinear wave dynamics, applied analysis, and the development of innovative methods for solving partial differential equations.

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