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Some Special Questions

  • W. I. Fushchich
  • W. M. Shtelen
  • N. I. Serov
Part of the Mathematics and Its Applications book series (MAIA, volume 246)

Abstract

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.

Keywords

Dirac Equation Schrodinger Equation Symmetry Operator Galilean Transformation Nonlinear Heat Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • W. I. Fushchich
    • 1
  • W. M. Shtelen
    • 1
  • N. I. Serov
    • 1
  1. 1.Institute of MathematicsKievUkraine

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