Affiliation:
1. Laboratoire de Mathématiques d'Orsay CNRS, Université Paris‐Saclay Orsay France
2. Department of Mathematics and Computer Science University of Basel Basel Switzerland
Abstract
AbstractWe study the Calogero–Moser derivative nonlinear Schrödinger NLS equation
posed on the Hardy–Sobolev space with suitable . By using a Lax pair structure for this ‐critical equation, we prove global well‐posedness for and initial data with sub‐critical or critical ‐mass . Moreover, we prove uniqueness of ground states and also classify all traveling solitary waves. Finally, we study in detail the class of multi‐soliton solutions and we prove that they exhibit energy cascades in the following strong sense such that as for every .
Funder
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Cited by
1 articles.
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