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arXiv · 2012.04805

Microscopic conservation laws for the derivative Nonlinear Schr\"{o}dinger equation

Xingdong Tang·Guixiang Xu
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Abstract

Compared with macroscopic conservation law for the solution of the derivative nonlinear Schr\"odingger equation (DNLS) with small mass in \cite{KlausS:DNLS}, we show the corresponding microscopic conservation laws for the Schwartz solutions of DNLS with small mass. The new ingredient is to make use of the logarithmic perturbation determinant introduced in \cite{Rybkin:KdV:Cons Law, Simon:Trace} to show one-parameter family of microscopic conservation laws of the $A(\kappa)$ flow and the DNLS flow, which is motivated by \cite{HKV:NLS,KV:KdV:AnnMath,KVZ:KdV:GAFA}.

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Xingdong Tang, Guixiang Xu. 2020-12-09. Microscopic conservation laws for the derivative Nonlinear Schr\"{o}dinger equation. https://arxiv.org/abs/2012.04805

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