|
This article is cited in 8 scientific papers (total in 8 papers)
The Dirac operator with elliptic potential
A. O. Smirnov St. Petersburg State Academy of Aerospace Equipment Construction
Abstract:
The Dirac operator with elliptic finite-gap potential
$$
-\mathrm i\begin{pmatrix}1&0\\0&-1\end{pmatrix}\Psi _x
+\begin{pmatrix}0&p\\q&0\end{pmatrix}\Psi =\lambda\Psi .
$$
is considered. An Ansatz for the Krichever curves associated with elliptic (in $x$) finite-gap solutions of the 'decomposed' non-linear Schrödinger equation
$$
\begin{cases}
\mathrm ip_t+p_{xx}-2p^2q=0, \\iq_t-q_{xx}+2pq^2=0
\end{cases}
$$
and of the modified $KdV$ ($mKdV$) equation
$$
\begin{cases}
p_t+p_{xxx}-6pqp_x=0, \\q_t+q_{xxx}-6pqq_x=0.
\end{cases}
$$
is presented. Examples of two- and three-sheeted coverings associated with the one- and twogap Dirac potential are discussed.
Received: 27.07.1994
Citation:
A. O. Smirnov, “The Dirac operator with elliptic potential”, Mat. Sb., 186:8 (1995), 133–141; Sb. Math., 186:8 (1995), 1213–1221
Linking options:
https://www.mathnet.ru/eng/sm64https://doi.org/10.1070/SM1995v186n08ABEH000064 https://www.mathnet.ru/eng/sm/v186/i8/p133
|
Statistics & downloads: |
Abstract page: | 318 | Russian version PDF: | 101 | English version PDF: | 21 | References: | 41 | First page: | 1 |
|