Iteration of some discretizations of the nonlinear Schrödinger equation (Q1115152)
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scientific article; zbMATH DE number 4086962
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Iteration of some discretizations of the nonlinear Schrödinger equation |
scientific article; zbMATH DE number 4086962 |
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Iteration of some discretizations of the nonlinear Schrödinger equation (English)
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1986
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We consider several discretizations of the nonlinear Schrödinger equation which lead naturally to the study of some symmetric difference equations of the form \(\phi_{n+1}+\phi_{n-1}=f(\phi_ n)\). We find a variety of interesting and exotic behaviour from simple closed orbits to intricate patterns of orbits and loops in the \((\phi_{n+1},\phi_ n)\) phase-plane. Some analytical results for a special case are also presented.
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iteration
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nonlinear Schrödinger equation
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symmetric difference equations
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orbits
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loops
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