Quartic normal forms for the periodic nonlinear Schrödinger equation with dispersion management

2004 ◽  
Vol 191 (3-4) ◽  
pp. 219-237 ◽  
Author(s):  
Panayotis Panayotaros
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Normal Forms ◽  
Nonlinear Schrodinger Equation ◽  
Dispersion Management ◽  
Nonlinear Schrödinger

THE ENERGY GRAPH OF THE NONLINEAR SCHRÖDINGER EQUATION, OPEN PROBLEMS

2013 ◽  
Vol 23 (04) ◽  
pp. 943-962 ◽  
Author(s):  
C. PROCESI
Keyword(s):  
Schrödinger Equation ◽  
Cayley Graph ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Normal Forms ◽  
State Of The Art ◽  
Nonlinear Schrodinger Equation ◽  
Open Problems ◽  
Nonlinear Schrödinger ◽  
The Moment

We discuss some combinatorial and algebraic problems which have arisen from the study of the nonlinear Schrödinger equation. In particular we discuss a combinatorial graph, which we call energy graph associated to a Cayley graph. Some important features of normal forms are hidden into properties of this graph. Some of these properties are at the moment only conjectural and we point out the state of the art.

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