Abstract:

Lie group analysis can be called a microscope of mathematical modelling. Just like use of microscope in biology, group analysis allows to reveal symmetries of nonlinear mathematical models that cannot be seen otherwise. Numerous physical phenomena can be investigated using Lie symmetries to unearth various group invariant solutions and conservation laws that provide significant physical insight into the problem. Moreover, group analysis helps to eliminate systematic increase of volume of information to be memorized by students and to reduce calculations significantly. For example, it reduces about 400 types of solvable differential equations, tabulated and widely used by teachers and engineers, to 4 equations only! Group analysis analysis makes mathematics easier and more attractive for engineering students. For example, the course Partial Differential Equations at Moscow Institute of Physics and Technology attracted more than 100 students when N.H.Ibragimov used Lie group methods, instead of 10 students in the traditional course. The same happened when N.H.Ibragimov delivered similar lectures for science students in South Africa and Sweden. In our laboratory, "Group analysis of mathematical models of natural science, engineering and technology," new mathematics courses for engineering students with the elements of group analysis are being developed.