Effects of nonlinear wave coupling: Accelerated solitons
Boomerons: From curiosity to nonlinear optics
Dipartimento di Fisica, Istituto Nazionale di Fisica Nucleare, Università “La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy
2 Dipartimento di Elettronica per l'Automazione, Università di Brescia, via Branze 38, 25123 Brescia, Italy
3 Institut Carnot de Bourgogne, UMR 5209 CNRS, Université de Bourgogne, 9 Av. A. Savary, BP. 46870, 21078 Dijon, France
Boomerons are described as accelerated solitons for special integrable systems of coupled wave equations. A general formalism based on the Lax pair method is set up to introduce such systems which look of Nonlinear Schrödinger-type with linear, quadratic and cubic coupling terms. The one-soliton solution of such general systems is also briefly discussed. We display special instances of wave systems which are of potential interest for applications, including dispersion-less models of resonating waves. Among these, special attention and details are given to the celebrated equations describing the resonant interaction of three waves, in view of their application to optical pulse propagation in quadratic nonlinear media. For this particular case, we present exact solutions of the three-wave resonant interaction system, in the form of triplets moving with a common nonlinear velocity (simultons). The simultons have nontrivial phase-fronts and exist for different velocities and energy flows. We studied simulton stability upon propagation, and found that solitons with a velocity greater than a certain critical value are stable. We explore a novel consequence of the particle-like nature of three-wave simultons, namely their inelastic scattering with particular linear waves. Such phenomenon is associated with the excitation (decay) of stable (unstable) simultons by means of the absorption (emission) of the energy carried by a particular isolated pulse. Inelastic processes are exactly described in terms of boomerons. We also briefly consider collisions between different three-wave simultons.
© EDP Sciences, Springer-Verlag, 2007