Bäcklund Transformation and L2-stability of NLS Solitons
Bäcklund Transformation and L2-stability of NLS Solitons
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DOI：
10.1093/imrn/rnr073
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发表时间：
2010-11
影响因子：
1
通讯作者：
Tetsu Mizumachi;D. Pelinovsky
中科院分区：
文献类型：
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作者：
Tetsu Mizumachi;D. Pelinovsky
L2-亚临界聚焦非线性薛定谔（NLS）方程的基态由于其变分特征而在能量类H1中是轨道稳定的。本文研究了一维三次NLS方程的1-孤子的L2轨道稳定性。此外，我们证明了，如果初始数据是在H3除了是小的L2，那么该解决方案保持在一个特定的1-孤子解的L2-邻域的所有时间。证明依赖于这个可积方程的零解和孤子解之间的Backlund变换。
Ground states of a L2-subcritical focusing nonlinear Schrodinger (NLS) equation are known to be orbitally stable in the energy class H1 thanks to its variational characterization. In this paper, we will show L2-orbital stability of 1-solitons to a one-dimensional cubic NLS equation for any initial data which are close to 1-solitons in L2. Moreover, we prove that if the initial data are in H3 in addition to being small in L2, then the solution remains in an L2-neighborhood of a specific 1-soliton solution for all the time. The proof relies on the Backlund transformation between zero and soliton solutions of this integrable equation.