Concentration of Coupled Cubic Nonlinear Schrdinger Equations
-
摘要: 在二维空间中考虑了一类非线性Schrdinger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.
-
关键词:
- 非线性Schrdinger方程 /
- 整体解 /
- 爆破 /
- 爆破点 /
- 集中
Abstract: A coupled nonlinear SchrL 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.-
Key words:
- nonlinear SchrL dinger equation /
- global existence /
- blow up /
- blow-up point /
- concentration
-
[1] Newboult G K,Parker D F,Fanlkner T R.Coupled nonlinear Schrdinger 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 Schrdinger equations and sharp interpolation estimates[J].Communications Mathematical Physics,1983,87(4):567—576. doi: 10.1007/BF01208265 [4] Merle F,Tsutumi Y.L2-concentration of blow-up solution for the nonlinear Schrdinger 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 Schrdinger Equations[M].Textos de Metodos Matematicos,26, Rio de Janero:Instituto de Mathmatica-UFRJ,1993.
计量
- 文章访问数: 2404
- HTML全文浏览量: 103
- PDF下载量: 628
- 被引次数: 0