Localized states in fluid convection and multi-photon lasers
The Weiss, Tabor, Carnevale (WTC) formalism for expanding a solution about a complex pole is used to determine various finite and infinite localized solutions to the Complex Ginzburg-Landau equation in parameter regimes corresponding to binary convection. The stability of the WTC soliton is analyzed, and the dimension of the null space of the stability operator is connected to a Painlevé extension of the WTC soliton. It is argued that this makes the WTC soliton very robust, which we proceed to demonstrate numerically. Numerical spike solutions are found which may be related to the infinite, but localized, WTC solutions. The relationship between the analytic solutions and physical experiments in fluids and lasers is discussed.
J. Powell and P.K. Jakobsen. “Localized states in fluid convection and multi-photon lasers,” Physica D 64, 132–52, 1993.