Large time behavior of solutions to the generalized derivative nonlinear Schrödinger equation
Large time behavior of solutions to the generalized derivative nonlinear Schrödinger equation
复制标题
广义导数非线性薛定谔方程解的大时间行为
DOI：
10.3934/dcds.1999.5.93
复制
发表时间：
1998
影响因子：
1.1
通讯作者：
P. Naumkin
中科院分区：
文献类型：
--
作者：
N. Hayashi;E. Kaikina;P. Naumkin
本文研究了一类非线性薛定谔方程的柯西问题
We study the Cauchy problem for a nonlinear Schrodinger equation which is
the generalization of a one arising in plasma physics. We focus on the so called subcritical
case and prove that when the initial datum is "small", the solution exists globally in time
and decays in time just like in the linear case. For a certain range of the exponent in
the nonlinear term, we prove that the solution is asymptotic to a "final state" and the
nonexistence of asymptotically free solutions. The method used in this paper is based on
some gauge transformation and on a certain phase function.