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The Cauchy Problem for Coupled Nonlinear Schrdinger Equations with Linear Damping： Local and Global Existence and Blowup of Solutions

The Cauchy Problem for Coupled Nonlinear Schrdinger Equations with Linear Damping: Local and Global Existence and Blowup of Solutions
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摘要 The authors study, by applying and extending the methods developed by Cazenave(2003), Dias and Figueira(2014), Dias et al.(2014), Glassey(1994–1997), Kato(1987), Ohta and Todorova(2009) and Tsutsumi(1984), the Cauchy problem for a damped coupled system of nonlinear Schrdinger equations and they obtain new results on the local and global existence of H^1-strong solutions and on their possible blowup in the supercritical case and in a special situation, in the critical or supercritical cases. The authors study, by applying and extending the methods developed by Cazenave（2003）, Dias and Figueira（2014）, Dias et al.（2014）, Glassey（1994–1997）, Kato（1987）, Ohta and Todorova（2009） and Tsutsumi（1984）, the Cauchy problem for a damped coupled system of nonlinear Schrdinger equations and they obtain new results on the local and global existence of H-1-strong solutions and on their possible blowup in the supercritical case and in a special situation, in the critical or supercritical cases.
作者 Joao-Paulo DIAS Mario FIGUEIRA Vladimir V. KONOTOP
机构地区 LCMAF-CIO Centro de Fisica Teorica e Computacional and Departamento de Fisica
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第5期665-682,共18页 数学年刊（B辑英文版）
基金 supported by the Fundacao para a Ciência e Tecnologia(Portugal)(Nos.PEstOE/MAT/UI0209/2013,UID/MAT/04561/2013,PTDC/FIS-OPT/1918/2012,UID/FIS/00618/2013)
关键词 爆破方案 柯西问题 耦合系统 非线性 整体存在性 线性阻尼 方程 超临界 supercritical Cauchy applying estimates proof admissible constants uniqueness nonlinearity inequality
分类号 O175.27 [理学—基础数学] TU746.5 [建筑科学—建筑技术科学]
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参考文献14

  • 1Bludov, Yu. V., Driben, R., Konotop, V. V. and Malomed, B. A., Instabilities, solitons and rogue waves in PT-coupled nonlinear waveguides, J. Opt., 15, 2013, 064010.
  • 2Cazenave, T., Semilinear SchrSdinger Equations, Courant Lecture Notes, Vol. 10, Amer. Math. Soc., 2003.
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  • 4Dias, J. P. and Figueira, M., On the blowup of solutions of a SchrSdinger equation with an inhomogeneous damping coefficient, Comm. Contemp. Math. 16, 2014, 1350036.
  • 5Dias, J. P., Figueira, M., Konotop, V. V. and Zezyulin, D. A., Supercritical blowup in coupled parity- time-symmetric nonlinear SchrSdinger equations, Studies Appl. Math., 133, 2014, 422-440.
  • 6Glassey, R. T., On the blowing up of solutions to the Cauchy problem for nonlinear SchrSdinger equations, J. Math. Phys., 18, 1977, 1794-1797.
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Chinese Annals of Mathematics,Series B
2016年 第5期

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