Manuscript Topics

In recent years, a lot of work has been devoted to the full comprehension of the geometrical and analytical structural properties of exactly solvable, integrable and superintegrable systems on various classes of spaces, both at the classical and quantum level. Several new connections with different areas, such as nonlinear differential equations, the theory of special functions and generalizations, as well as algebraic structures beyond Lie algebras have emerged from this work, providing alternative techniques and tools complementary to the traditional analytical approach, and pointing out new applications to various real-world problems.

The aim of this special issue is to report on recent advances related to (super-)integrability in terms of the Lie group analysis, with special emphasis on new applications in several fields of natural sciences and engineering. We are interested in high-quality papers that contain original research results and techniques that provide some insight on the interplay between integrability, Lie theoretical methods and various subfields of mathematics and physics. Potential topics include, but are not limited to:

• Classical and quantum integrable systems
• Classical and quantum superintegrable systems
• Lie systems, Lie-Hamilton systems, Dirac systems and generalizations
• Generalized symmetries and conservation laws of differential equations
• Algebraic methods in representation theory related to integrability
• Topological methods in integrability

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