Large time asymptotics of solutions for the third-order nonlinear Schrodinger equation

JMS
Vol. 23 (2016), No. 4, Page 867–919.

Hayashi, Nakao ; Naumkin, Pavel I..
Large time asymptotics of solutions for the third-order nonlinear Schrodinger equation
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Abstract:
We study the large time asymptotics of small amplitude solutions to the Cauchy problem for the third-order nonlinear Schr\"{o}dinger equation with zero mass condition which is considered as a complex version of the modi ed Korteweg-de Vries equation. We apply the factorization of the free evolution group to improve the time decay estimate of solutions obtained in the previous work.

Keywords: Third-order nonlinear Schr\"{o}dinger equation; Large time behavior of solutions; Complex modifed Korteweg-de Vries equation.

Mathematics Subject Classification (2010): 35Q35, 35Q55
Mathematical Reviews Number: MR3588264

Received: 2015-12-07