Manuscript Topics

Many real-world problems, which arise in various scientific fields such as economics, biology, fluid dynamics, physics, engineering, control theory, materials science, quantum mechanics, and in industry are modelled by physically and mathematically interesting nonlinear differential equations. Exact solutions of nonlinear differential equations graphically illustrate and provide us the mechanisms of many complex nonlinear phenomena. Exact solutions can also be used as “test problems” to establish the stability and estimate errors of many numerical and analytical methods.

Over the past years, several methods have been developed to construct exact solutions of such nonlinear differential equations. However, Lie symmetry analysis is a powerful and effective tool which can produce exact solutions of nonlinear differential equations. The aim of this special issue will be to report on recent developments in Lie symmetry analysis and conservation laws for solving such nonlinear differential equations as well as their new applications in several fields of natural sciences and engineering. We are interested in high-quality papers that contain original research results.

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