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Center for Nonlinear Studies |
Resonance interaction of light with atoms is described by the Maxwellloch system of equations. These equations are known to be integrable by the Inverse Scattering Tranform (IST) which is an appropriate method for finding solutions of an initial value problem. The IST is known to be the nonlinear generalization of the Fourier method. In real physical situations describing interaction of an active medium with an incident light pulse we are lead to consider a problem with both initial conditions and boundary values. In this case, the IST is not sufficient for solving the problem. For linear equations this type of problem can be solved using the method of characteristics (d'Alembert method). We find the nonlinear generalization of this method using analytic properties of associated operators, and we describe the solution of the problem.
Host: Ildar Gabitov