# American Institute of Mathematical Sciences

March  2017, 37(3): 1295-1321. doi: 10.3934/dcds.2017054

## Modified energy functionals and the NLS approximation

 Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA

Received  June 2016 Revised  November 2016 Published  December 2016

We consider a model equation from [14] that captures important properties of the water wave equation. We give a new proof of the fact that wave packet solutions of this equation are approximated by the nonlinear Schrödinger equation. This proof both simplifies and strengthens the results of [14] so that the approximation holds for the full interval of existence of the approximate NLS solution rather than just a subinterval. Furthermore, the proof avoids the problems associated with inverting the normal form transform in [14] by working with a modified energy functional motivated by [1] and [8].

Citation: Patrick Cummings, C. Eugene Wayne. Modified energy functionals and the NLS approximation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1295-1321. doi: 10.3934/dcds.2017054
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##### References:
Partition of k$\ell$ -plane.
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