The Route of Cavitation in the Laser-plasma Interaction: Integrable Model

In the context of laser-plasma interaction, a model accounting for the localization of energy due to an “extrinsic” nonlinearity is derived. This model is shown to be integrable by means of the Spectral Transform Theory with a singular dispersion relation. The integrability is shown to be independent of initial conditions. An exact singular asymptotic solution is obtained. A physical interpretation of the solution is given.