一类耦合非线性Schr?dinger方程组的集中现象

基金项目: 国家自然基金资助项目(10271084);四川省重点实验室四川师范大学计算机软件实验室基金资助项目

Concentration of Coupled Cubic Nonlinear Schrdinger Equations

College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China;

摘要: 在二维空间中考虑了一类非线性Schrdinger方程组．在能量守恒及质量守恒的基础上,通过对解的极限行为的研究,建立了一系列解在原点的局部恒等式,得到了方程组的径向对称爆破解的集中性质．
- 非线性Schrdinger方程 /
- 整体解 /
- 爆破 /
- 爆破点 /
- 集中
Abstract: A coupled nonlinear Schr^L dinger equations is considered in 2-D space. Based upon the conservation of mass and energy, local identities was established by the study of the limit behavior of the solutions, and concentration for the blow-up solutions with radially symmetry was obtained.
- nonlinear Schr^L dinger equation /
- global existence /
- blow up /
- blow-up point /
- concentration

[1]	Newboult G K,Parker D F,Fanlkner T R.Coupled nonlinear Schrdinger equations arising in the study of monomode step-index opitical fibers[J].Journal of Mathematical Physics,1989,30(4):930—936. doi: 10.1063/1.528360
[2]	Hayata K,Koshiba M.Multidimensional solutions in cubic nonlinear media[J].Optics Letters,1994,19(21):1717—1719. doi: 10.1364/OL.19.001717
[3]	Weinstein M I.Nonlinear Schrdinger equations and sharp interpolation estimates[J].Communications Mathematical Physics,1983,87(4):567—576. doi: 10.1007/BF01208265
[4]	Merle F,Tsutumi Y.L2-concentration of blow-up solution for the nonlinear Schrdinger equations with the critical power nonlinearity[J].Journal of Differential Equations,1990,84(2):205—214. doi: 10.1016/0022-0396(90)90075-Z
[5]	Weinstein M I.On the structure and formation singularities in solutions to nonlinear dispersive evolution equations[J].Communications in Partial Differential Equations,1986,11(5):545—565. doi: 10.1080/03605308608820435
[6]	ZHANG Jian.Instability of optical solitions for two-wave interaction model in cubic nonlinear media[J].Advance in Mathematical Sciences and Applications,1998,8(2):691—713.
[7]	Strauss W A.Existence of solitary waves in higher dimensions[J].Communications Mathematical Physics,1977,55(1):149—162. doi: 10.1007/BF01626517
[8]	Cazenave T.An Introduction to Nonlinear Schrdinger Equations[M].Textos de Metodos Matematicos,26, Rio de Janero:Instituto de Mathmatica-UFRJ,1993.

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