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Modified energy functionals and the NLS approximation

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  • 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].

    Mathematics Subject Classification: 35L72, 35Q55, 70K30, 70K45, 35Q35.


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  • Figure 1.  Partition of k$\ell$ -plane.

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