Nonlinear and Noncommutative Mathematics are rapidly developing versatile subjects. In the last decade, there have emerged new concepts and methods, and diverse applications in theoretical physics, particularly to the understanding of aspects of quantum theory and high-energy physics.

The rapid evolution of the mathematical foundations and tools, including new paradigms that are influencing our community and frameworks that can be generalized in many directions, suggests the value of a special issue devoted to such applications.

This special issue will focus on all aspects of Nonlinear and Noncommutative Mathematics, from their foundations to applications in theoretical physics. We invite authors to present original research articles as well as review articles that will be representative of the state of the art in the field. The topics to be covered include, but are not limited to:

• Quantum field theory and noncommutative geometry
• Coherent states and related representations
• Quantum groups, algebras, and quantum special functions
• Nonlinear partial differential equations