Solitons in real fluids

Abstract

Solitons were discovered and their properties described in the study of ideal, dissipation-free non-linear integrable systems such as the Korteweg-de Vries equation and Toda's lattice. Originally appearing as solitary waves, their peculiar properties of invariance upon translation and their typical elastic collisions with at most a phase shift in trajectories led quite correctly to them being considered particle like. Indeed they behave as 'perfect' particles/molecules/hard spheres. What about real, dissipative media such as a sheared, stably stratified atmosphere or open shallow liquid layers heated from the air side? In the latter case I illustrate how following an instability threshold solitons can be created and maintained thanks on the one hand to a (local) balance between (inertial) non-linearity and dispersion and on the other hand to an input-output (pumping-dissipation) energy balance. Theory and numerical and experimental evidence illustrate the features of such 'imperfect'/van der Waals-like molecules: head-on and oblique elastic or inelastic collisions, wall reflections with and without formation of Mach stems, etc.