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The Research Summary of the Properties of the Blow-up Solutions for a Nonlinear Schr(?)dinger Equation

Author: HuWenYan
Tutor: ZhangKaiJun
School: Northeast Normal University
Course: Operational Research and Cybernetics
Keywords: Blow up of Solutions Blow up Rate Self-similarity L ~ 2 - concentration in
CLC: O175.2
Type: Master's thesis
Year: 2007
Downloads: 82
Quote: 0
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Abstract


Nonlinear Schrodinger equation is the basic equation of quantum mechanics , it comes from quantum field theory , in particular, the Hartree-Fock theory . From a mathematical point of view , it also has the parabolic equations and hyperbolic equations similar nature . In recent years , the nonlinear Schrodinger equation by many mathematicians . Not only because it reveals the basic law of the microscopic physical world of physical movement , has a wide range of applications in the field of nonlinear optics , but also because there are a lot of model simplified , are to determine the nonlinear Schrodinger equation . Of the nonlinear Schrodinger equation Blowup Properties Research : First, a systematic solution of the nonlinear Schrodinger equation in variation limited variation unlimited and the anisotropy function space case , under what circumstances will burst ; and a class of quasilinear Schr?dinger equation , for example , to discuss a solution blasting , to promote the results of the previous quasilinear Schr?dinger equation in anisotropic function space solution for a limited time within it will explode . Second, the nature of the bursting of the solution ( solution blasting rate , self- similarity , L to 2 - concentration ) conducted a detailed analysis . Finally, several unresolved issues .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations
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