Variational principles, Lie point symmetries, and similarity solutions of the vector Maxwell equations in nonlinear optics
The authors formulate the vector Maxwell equations coupled to a single Lorentz oscillator with instantaneous Kerr nonlinearity in terms of Lagrangian and Hamiltonian variational principles. Four conservation laws for these equations are obtained. The traveling wave solutions and the kink solutions are investigated. It was obtained that the smooth periodic traveling wave solutions develop very steep electric field gradients as the dimensionless wave velocity tends to 1 from above, and the method of extending them into the slower velocity regime is demonstrated. It was also obtained that the kink and anti-kink solutions exist only for a restricted range of traveling wave velocities. These solutions may be used in switching devices or in optical computing.
scientific article; zbMATH DE number 2117600
scientific article