New Conservation Laws and Energy Cascade for 1d Cubic NLS and the Schr\"odinger map
Valeria Banica, Luis Vega
TL;DR
This paper reviews recent findings on the 1d-cubic NLS and Schr"odinger Map, highlighting new conservation laws, an energy cascade, and novel examples of the Talbot effect at critical regularity.
Contribution
It introduces new conservation laws and demonstrates an energy cascade for 1d-cubic NLS and Schr"odinger Map, along with examples of the Talbot effect at critical regularity.
Findings
Existence of an energy cascade in Schr"odinger Map
New conservation laws for 1d-cubic NLS
Examples of Talbot effect at critical regularity
Abstract
We review some recent results concerning the Initial Value Problem of 1d-cubic non-linear Schr\"odinger equation (NLS) and other related systems as the Schr\"odinger 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.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Black Holes and Theoretical Physics · Computational Fluid Dynamics and Aerodynamics