Some Special Questions
In the present chapter we consider some problems tightly connected with group-algebraic investigations such as: finding nonlocal transformations to linearize a given nonlinear PDE, symmetry analysis of the three-body problem, calculating final transformations generated by non-Lie symmetry operators, and studying symmetry of integrodifferential equations. Here we introduce the concept of conditional invariance, and study non-Lie symmetry of quasi-relativistic generalization of the Schrödinger equation, Galilean invariance of Maxwell’s equations, solutions of the Schrödinger equation invariant under the non-Lie Lorentz algebra. Finally, in the concluding topic we introduce the concept of approximate symmetry.
KeywordsDirac Equation Schrodinger Equation Symmetry Operator Galilean Transformation Nonlinear Heat Equation
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