A robust way to justify the derivative NLS approximation

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) NLS equations (nonlinear Schrödinger equations) (35Q55) Theoretical approximation in context of PDEs (35A35) Perturbations in context of PDEs (35B20) Cauchy-Kovalevskaya theorems (35A10) Resonance in context of PDEs (35B34) Traveling wave solutions (35C07)

Cites Work

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Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth
The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions
A rigorous justification of the modulation approximation to the 2D full water wave problem
Global well-posedness on the derivative nonlinear Schrödinger equation
Global well-posedness for the derivative nonlinear Schrödinger equation in \(H^{\frac {1}{2}} (\mathbb{R})\)
Modified energy functionals and the NLS approximation
A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves
On the derivative nonlinear Schrödinger equation
The Cauchy problem for quasi-linear symmetric hyperbolic systems
Justification of modulation equations for hyperbolic systems via normal forms
Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity
Existence of long time solutions and validity of the nonlinear Schrödinger approximation for a quasilinear dispersive equation
Validity of the nonlinear Schrödinger approximation for the two-dimensional water wave problem with and without surface tension in the arc length formulation
Justification of the nonlinear Schrödinger approximation for a quasilinear Klein-Gordon equation
The NLS approximation for two dimensional deep gravity waves
Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances
Justification of the 2D NLS equation for a fourth order nonlinear wave equation - quadratic resonances do not matter much in case of analytic initial conditions
ASYMPTOTIC DECAY OF A ONE-DIMENSIONAL WAVE PACKET IN A NONLINEAR DISPERSIVE MEDIUM
The validity of modulation equations for extended systems with cubic nonlinearities
An exact solution for a derivative nonlinear Schrödinger equation
Growth and Decay of Acceleration Waves in Incompressible Saturated Poroelastic Solids
Nonlinear PDEs
A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative
Validity and Limitation of the Newell‐Whitehead Equation
The derivative nonlinear Schrödinger equation: Global well-posedness and soliton resolution
A proof of validity for multiphase Whitham modulation theory
Failure of the N‐wave interaction approximation without imposing periodic boundary conditions