Local well-posedness for the Zakharov system on the background of a line soliton

Hung Luong

doi:10.3934/cpaa.2018126

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2018, Volume 17, Issue 6: 2657-2682. Doi: 10.3934/cpaa.2018126

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Local well-posedness for the Zakharov system on the background of a line soliton

Hung Luong

Fak. Mathematik, University of Vienna, Oskar MorgensternPlatz 1, A-1090 Wien, Austria

Received: March 2018

Revised: March 2018

Published: June 2018

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Abstract

We prove that the Cauchy problem for the two-dimensional Zakharov system is locally well-posed for initial data which are localized perturbations of a line solitary wave. Furthermore, for this Zakharov system, we prove a weak convergence to a nonlinear Schrödinger equation.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35Q55.

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References

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