Decaying Long-Time Asymptotics for the Focusing NLS Equation with Periodic Boundary Condition

被引:26
|
作者
de Monvel, Anne Boutet [1 ]
Kotlyarov, Vladimir [2 ]
Shepelsky, Dmitry [2 ]
机构
[1] Univ Paris Diderot, IMJ, F-75013 Paris, France
[2] Inst Low Temp Phys, Div Math, UA-61103 Kharkov, Ukraine
关键词
NONLINEAR SCHRODINGER-EQUATION; MKDV EQUATION;
D O I
10.1093/imrn/rnn139
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the initial boundary value problem for the focusing nonlinear Schrodinger equation in the quarter plane x > 0, t > 0 in the case of decaying initial data (for t = 0, as x -> +infinity) and Dirichlet boundary data (for x = 0) approaching a periodic (single-frequency) background ae(2i omega t) as t -> +infinity. We first provide admissibility conditions for the normal derivative of the solution on the boundary, under the assumption that it behaves asymptotically in a similar (single-frequency) manner. We then show that for the range omega >= a(2)/2, the long-time asymptotics of the solution inside the quarter plane exhibits decaying oscillations of Zakharov-Manakov type.
引用
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页码:547 / 577
页数:31
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