The validity of the derivative NLS approximation for systems with cubic nonlinearities

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations in context of PDEs (35B20) Time-dependent Schrödinger equations and Dirac equations (35Q41) Classical solutions to PDEs (35A09)

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
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Modified energy functionals and the NLS approximation
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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 robust way to justify the derivative NLS approximation
Failure of the N‐wave interaction approximation without imposing periodic boundary conditions
Validity of the nonlinear Schrödinger approximation for quasilinear dispersive systems with more than one derivative

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