Solitoni in fluidi e superfluidi

In this thesis solitonic solutions have been studied for two systems very different from each other: fluids and superfluids. In the first chapter, the Korteweg-de Vries equation is derived in a characteristic form for an ideal fluid, starting from the study of superficial waves in shallow waters. In the second chapter, the Gross-Pitaevskii time-dependent equation is derived, starting from the Hamiltonian of N bosons at 0K temperature interacting with each other through a potential. In chapter three, bright solitons have been studied both for the KdV equation and for the GP time-dependent equation, finding their analitycal form.