Breathers are localized vibrational wave packets that appear in nonlinear systems, that is almost any physical system, when the perturbations are large enough for the linear approximation to be valid.
To be observed in a physical system, breathers should be stable. In this talk, there will be presented some results about the stability properties of breather solutions of different continuous models driven by nonlinear PDEs.
It will be shown how to characterize variationally the breather solutions of some nonlinear PDEs both in the line and in periodic settings.
Two specific examples will be analyzed:
a) the mKdV equation, it model waves in shallow water, and the evolution of closed curves and vortex patches.
b) the sine-Gordon equation: it describes phenomena in particle physics, gravitation, materials and many other systems.