$H^s$ 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 (5)

• Global well-posedness on the derivative nonlinear Schrödinger equation revisited
• Conserved energies for the cubic NLS in 1-d
• Complete integrability of derivative nonlinear Schrödinger-type equations
• Global well-posedness for the derivative nonlinear Schrödinger equation
• Optimal local well-posedness for the periodic derivative nonlinear Schrodinger equation

Cited by in corpus (13)

• Global well-posedness for the derivative nonlinear Schrödinger equation
• On the well-posedness problem for the derivative nonlinear Schrödinger equation
• A priori estimates for the derivative nonlinear Schrödinger equation
• On the global well-posedness of the Calogero-Sutherland derivative nonlinear Schrödinger equation
• On the stability of periodic waves for the cubic derivative NLS and the quintic NLS
• 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
• The stability of degenerate solitons for derivative nonlinear Schrodinger equations
• On the derivative nonlinear Schr{ö}dinger equation on the half line with Robin boundary condition
• Instability of degenerate solitons for nonlinear Schrödinger equations with derivative
• Well-posedness of the Cauchy Problem for the Kinetic DNLS on $\mathbf{T}$
• Nowhere continuity of the flow map of an integrable derivative nonlinear Schrödinger system on the torus