New Conservation Laws and Energy Cascade for 1d Cubic NLS and the Schrödinger Map
摘要
We recall some recent results concerning the Initial Value Problem of 1d-cubic non-linear Schrödinger equation (NLS) and other related systems as the Schrödinger Map. For the latter we prove the existence of a cascade of energy. Finally, some new examples of the Talbot effect at the critical level of regularity are given.