The energy graph of the nonlinear Schrödinger equation, open problems (Q2842027)
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scientific article; zbMATH DE number 6192881
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The energy graph of the nonlinear Schrödinger equation, open problems |
scientific article; zbMATH DE number 6192881 |
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30 July 2013
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non-linear PDEs
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combinatorics
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The energy graph of the nonlinear Schrödinger equation, open problems (English)
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Based on previous works of the author [with \textit{M. Procesi}, Commun. Math. Phys. 312, No. 2, 501--557 (2012; Zbl 1277.35318); with \textit{M. Procesi} and \textit{B. Van Nguyen}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 24, No. 2, 229--301 (2013; Zbl 1294.35146)] for the nonlinear Schrödinger equation (NLS) on the torus \(\mathbb{T}^n\), \(n \in \mathbb{N}\), it is introduced a combinatorial graph, properties of which turn out to be connected with normal forms of NLS in the Fourier representation and their solutions properties. The author presents here some new properties of this graph and corresponding properties of NLS solutions, some of which are only conjectural.
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