Guest Editor(s)
Prof. Kangjia Wang
Email: konka05@163.com
Affiliation: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo, China
Homepage:
Research Interests: soliton theory and integrable systems, machine learning and neural computing
Summary
Solitons are fundamental nonlinear wave structures that arise from the delicate balance between nonlinearity and dispersion. Since their discovery, soliton theory has become an important branch of nonlinear science. Fluid dynamics provides one of the most important physical backgrounds for the development and application of soliton theory. Various nonlinear wave phenomena, including solitary waves, multi-soliton interactions, breathers, rogue waves, kink waves, lump waves, and other localized coherent structures, play significant roles in shallow-water dynamics, internal waves, stratified fluids, geophysical flows, and other nonlinear fluid systems. Therefore, soliton theory and nonlinear-wave dynamics provide a natural framework for addressing a broad range of problems involving interfacial phenomena, multiphase flows, stratified and non-Newtonian fluids, and other complex fluid systems of relevance to engineering and materials processing.
Recent advances in nonlinear mathematical methods, integrable systems, symbolic computation, and numerical simulations have greatly promoted the study of nonlinear wave structures in fluid dynamics. In particular, the construction of exact and approximate solutions, the investigation of interaction dynamics, and the exploration of the physical mechanisms underlying nonlinear localized waves continue to attract considerable attention.
This Special Issue aims to bring together recent developments in soliton theory, nonlinear waves, and advanced computational methods in fluid dynamics. Original research articles and high-quality review papers are welcome.
Topics include, but are not limited to:
* Solitary waves and soliton theory in fluid dynamics;
* Mathematical theory of solitons and nonlinear waves;
* Mathematical models of nonlinear water waves;
* Nonlinear dispersive waves in complex fluid systems;
* Painlevé analysis, Lax Paris and integrability;
* Exact and approximate solutions of nonlinear evolution equations;
* Analytical and symbolic computational methods;
* Stability, Chaos and bifurcations of the nonlinear wave equations;
* Fractal and fractional calculus in soliton solutions;
* Hybrid nonlinear wave structures and interaction solutions;
* Variational theory in fluid dynamics;
* Numerical methods for nonlinear wave equations;
* Physics-informed neural networks (PINNs) for nonlinear wave equations and fluid dynamics;
* Deep learning and neural network approaches for soliton modeling and prediction;
* Neural network-based methods for solving NPDEs in fluid dynamics.
Keywords
fluid soliton dynamics, exact and approximate solutions, physics-informed neural networks, symbolic computation; integrability
Login
Register
Submit a Paper
Propose a Special lssue