The Calogero–Moser derivative nonlinear Schrödinger equation
Patrick D. Gerard, Enno Lenzmann
Abstract
Abstract We 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 .
Topics & Concepts
MathematicsSobolev spaceUniquenessNonlinear Schrödinger equationNonlinear systemSolitonSchrödinger equationSpace (punctuation)Derivative (finance)Mathematical analysisClass (philosophy)Schrödinger's catMathematical physicsPhysicsQuantum mechanicsEconomicsArtificial intelligenceLinguisticsFinancial economicsComputer sciencePhilosophyNonlinear Waves and SolitonsAdvanced Mathematical Physics ProblemsNonlinear Photonic Systems