$H^s$ Bounds for the Derivative Nonlinear Schrödinger Equation

Abstract

We study the derivative nonlinear Schrödinger equation on the real line and obtain global-in-time bounds on high order Sobolev norms.

20 pages

References in corpus (1)

• Global well-posedness for the derivative nonlinear Schrödinger equation

Cited by in corpus (11)

• Global well-posedness for the derivative nonlinear Schrödinger equation
• On the well-posedness problem for the derivative nonlinear Schrödinger equation
• On the global well-posedness of the Calogero-Sutherland derivative nonlinear Schrödinger equation
• Global Dynamics of small data solutions to the Derivative Nonlinear Schrödinger equation
• Microscopic conservation laws for the derivative Nonlinear Schrödinger equation
• Asymmetric integrable turbulence and rogue wave statistics for the derivative nonlinear Schrödinger equation
• On the derivative nonlinear Schr{ö}dinger equation on the half line with Robin boundary condition
• The stability of degenerate solitons for derivative nonlinear Schrodinger equations
• Well-posedness of the Cauchy Problem for the Kinetic DNLS on $\mathbf{T}$
• Instability of degenerate solitons for nonlinear Schrödinger equations with derivative
• Nowhere continuity of the flow map of an integrable derivative nonlinear Schrödinger system on the torus