Meromorphic solutions to a differential-difference equation describing certain self-similar potentials (Q2757145)
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scientific article; zbMATH DE number 1675931
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Meromorphic solutions to a differential-difference equation describing certain self-similar potentials |
scientific article; zbMATH DE number 1675931 |
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Meromorphic solutions to a differential-difference equation describing certain self-similar potentials (English)
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21 October 2002
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meromorphic solutions
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Schrödinger operator
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differential-difference equations
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selfsimilar potentials
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The paper is devoted to nonlinear differential-difference equations describing certain selfsimilar potentials for the Schrödinger operator of the form NEWLINE\[NEWLINE\bigl[f(x)+ f(x+a)\bigr]' +f^2(x)-f^2(x+a)= \mu,NEWLINE\]NEWLINE where \(a\) and \(\mu\) are some complex constants. The existence of meromorphic solutions with simple poles in the case \(\mu\neq 0\) is proved. These solutions have the additional property that there are no singularities on the real axis.
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