Stability of KAM Tori for Nonlinear Schrodinger Equation, Hongzi Cong, Jianjun Liu, Xiaoping Yuan

Автор: Fibich Gadi
Название: Nonlinear Schrodinger Equation
ISBN: 3319127470 ISBN-13(EAN): 9783319127477
Издательство: Springer
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Описание: The Nonlinear Schrodinger Equation

Автор: M. Escobedo, J. J. L. Velazquez
Название: On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation
ISBN: 1470414341 ISBN-13(EAN): 9781470414344
Издательство: Mare Nostrum (Eurospan)
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Описание: Examines the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrodinger equation. The authors define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained.

Автор: Agmon Shmuel
Название: Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. (MN-29)
ISBN: 0691613672 ISBN-13(EAN): 9780691613673
Издательство: Wiley
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Описание: Mathematical Notes, 29 Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paper

Автор: Yulia Karpeshina, Roman Shterenberg
Название: Extended States for the Schrodinger Operator with Quasi-Periodic Potential in Dimension Two
ISBN: 1470435438 ISBN-13(EAN): 9781470435431
Издательство: Mare Nostrum (Eurospan)
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Описание: Considers a Schrodinger operator $H=-\Delta +V(\vec x)$ in dimension two with a quasi-periodic potential $V(\vec x)$. The authors prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties.

Автор: Gabriella Pinzari
Название: Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem
ISBN: 1470441020 ISBN-13(EAN): 9781470441029
Издательство: Mare Nostrum (Eurospan)
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Описание: Proves the existence of an almost full measure set of $(3n-2)$-dimensional quasi-periodic motions in the planetary problem with $(1+n)$ masses, with eccentricities arbitrarily close to the Levi-Civita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed.

Автор: Xiao Xiong, Quanhua Xu, Zhi Yin
Название: Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori
ISBN: 1470428067 ISBN-13(EAN): 9781470428068
Издательство: Mare Nostrum (Eurospan)
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Описание: Gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative $d$-torus $\mathbb{T}^d_\theta$ (with $\theta$ a skew symmetric real $d\times d$-matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincare type inequality for Sobolev spaces.