Differential equations govern many phenomena that happen in the nature and play an important role in the progress of engineering and technology. Essentially all the fundamental equations are nonlinear, and, in general, such nonlinear equations are often very difficult to solve explicitly. Symmetry group techniques provide methods to obtain solutions of these equations. These methods have several applications, for example, in the study of nonlinear partial differential equations, that admit conservation laws which arise in many disciplines of the applied sciences.

Recent studies show that infinitely many nonlocal symmetries of various integrable models are related to their Lax pairs. Symmetry method is one of the most powerful tools that give out new integrable models from known ones. Integrable models have played an important role in applied sciences and are one of the central topics in soliton theory. In order to know if a system is integrable, it is very important to study Lax pairs of the system.

A symmetry can be considered as an equivalence transformation which leaves invariant not only the differential structure of equation but also the form of the arbitrary elements. This fact made Ovsiannikov search for equivalence transformations in a systematic way by using an algorithm based on the extension of the Lie infinitesimal criterion. When an equation contains an arbitrary function, it reflects the individual characteristic of phenomena belonging to a large class. In this sense, the knowledge of equivalence transformations can provide us with certain relations between the solutions of different phenomena of the same class.

We invite authors to present original research articles as well as review articles. This special issue is devoted to recent advances in symmetry groups, equivalence transformations, Lax Pairs, and conservation laws for differential equations. Potential topics include, but are not limited to:

• Advance research and theoretical analysis in group analysis and differential equations
• The Noether symmetries, applications, and conservation laws
• Numerical algorithms concerning the symmetry groups for partial differential equations
• New and direct methods to obtain exact explicit solutions for differential equations

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