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Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line

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  • We prove the unconditional uniqueness of solutions to the derivative nonlinear Schrödinger equation (DNLS) in an almost end-point regularity. To this purpose, we employ the normal form method and we transform (a gauge-equivalent) DNLS into a new equation (the so-called normal form equation) for which nonlinear estimates can be easily established in $ H^s({\mathbb{R}}) $, $ s>\frac12 $, without appealing to an auxiliary function space. Also, we prove that low-regularity solutions of DNLS satisfy the normal form equation and this is done by means of estimates in the $ H^{s-1}({\mathbb{R}}) $-norm.

    Mathematics Subject Classification: 35Q55.


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