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Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

Regardez les singularit es: il n y a que ca, qui compte. Gaston Julia The nonlinear Schr] odinger (NLS) equation provides a canonical descr- tion for the envelope dynamics of a quasi-monochromatic plane wave (the carrying wave) propagating in a weakly nonlinear dispersive medium when dissipative processes are negligible. On short times and small propagation distances, the dynamics are linear, but cumulative nonlinear interactions result in a signi?cant modulation of the wave amplitude on large spatial and temporal scales. The NLS equation expresses how the linear dispersion relation is...