Waves exist widely in various fields of physics, such as fluids, plasmas, acoustics, optics, or electromagnetism. These phenomena can usually be described by differential equations and the corresponding solving methods are fundamentally challenging. The analytical methods and numerical techniques used to solve differential equations in mathematics have been developing rapidly, however there are still many difficulties, regardless of whether the nonlinear partial differential equations are integrable.

In addition, explaining the physical characteristics and mechanisms of waves is also critical. Different concepts, such as solitons, breathers, and rogue waves have been introduced and intensively discussed. The theory and application of nonlinear waves has attracted great interest and needs to be further studied.

This Special Issue aims to show the latest advances in nonlinear waves and differential equations, whether the results are theoretical or numerical. We welcome both original research and review articles relating to solitons, breathers, and rogue waves in continuous or discrete nonlinear systems. Interactions between different types of waves are considered valuable. Chaotic and random behaviours in nonlinear differential equations are also within the scope of the Special Issue. Mathematical tools dealing with nonlinear differential equations would also be meaningful additions.

Potential topics include but are not limited to the following:

• Solitons, breathers, and rogue waves
• Waves in fractional systems
• Theoretical and experimental methods of nonlinear waves
• Nonlinear energy sinks and nonlinear resonance in acoustics
• Quantum computing and quantum spin waves
• Integrable and nonintegrable differential equations
• Chaos and fractals in nonlinear dynamical systems
• Symbolic and numerical methods