Nonlinear group representations and applications to nonlinear equations
The group of time evolution of relativistic wave equations is contained in nonlinear representations of the Poincaré group. A general exposition of non linear representations of Lie groups is surveyed in order to exhibit the principal tools concerning the qualitative aspects of the theory. Examples of applications to nonlinear wave equations, such as the existence of global solutions, are then exposed. The main examples are nonlinear relativistic equations and Korteweg-de Vries equation.
KeywordsWave Equation Linear Representation Unitary Representation Nonlinear Representation Nonlinear Wave Equation
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- 1.M.FLATO,J.SIMON,G.PINCZON: “Nonlinear representations of Lie groups”. Ann. Scient. Ec. Norm. Sup. 10 (1977),405–418.Google Scholar
- 2.M.FLATO,J.SIMON: “Nonlinear equations and covariance”. Letters in Math.Phys. 2 (1977) 155–160.Google Scholar
- 3.M.FLATO, J.SIMON: “Yang-Mills equations are formally linearizable”. Letters in Math. Phys. 3 (1979) 279–283.Google Scholar
- 4.G. PINCZON, J. SIMON: “Models of nonlinear representations and examples of linearization techniques”. Preprint, Université de Dijon (1981).Google Scholar
- 5.J.SIMON: “Nonlinear representations of Poincaré group and global solutions of relativistic wave equations”. Preprint, Université Dijon (1981).Google Scholar
- 6.E.TAFLIN: “Analytic linearization of the KdV equation”. Preprint, Université de Genève (1981).Google Scholar