Using the Lagrangian formalism, with a simple trial function for dissipative optical two-dimensional 2D soliton beams, we show that there are two disjoint sets of stationary soliton solutions of the complex cubicquintic Ginzburg-Landau equation, with concave and convex phase profiles, respectively. These correspond to continuously self-focusing and continuously self-defocusing types of 2D solit...

We give a complete characterisation of the sets in which Peano derivatives of functions, which are definable in an o-minimal expansion of a real closed field, are continuously respectively Fréchet differentiable.