Nonlinear model of Schrödinger type: conservation laws, Hamiltonian structure, and complete integrability (Q1822283)
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scientific article; zbMATH DE number 4002697
| Language | Label | Description | Also known as |
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| English | Nonlinear model of Schrödinger type: conservation laws, Hamiltonian structure, and complete integrability |
scientific article; zbMATH DE number 4002697 |
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Nonlinear model of Schrödinger type: conservation laws, Hamiltonian structure, and complete integrability (English)
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1985
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A method is proposed for finding Lax type representations for nonlinear evolution (one-dimensional) equations of mathematical physics. It is shown that the Schrödinger-type nonlinear model \(\psi_ t- i\psi_{xx}+2| \psi |^ 2\psi_ x=0\) admits a Lax-type representation and is a Hamiltonian completely integrable dynamical system. Exact quasiperiodic (finite-gap, i.e., having only a finite number of stability bands in its spectrum) solutions of this system are obtained in terms of Riemann theta functions.
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Lax type representations
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nonlinear evolution
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Schrödinger-type nonlinear model
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Hamiltonian completely integrable
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Riemann theta functions
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