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This article is cited in 72 scientific papers (total in 72 papers)
Schrödinger operators with finite-gap spectrum and $N$-soliton solutions of the Korteweg–de Vries equation
A. R. Its, V. B. Matveev
Abstract:
Explicit description of periodic potentials for which the corresponding Schrodinger
operator $N$ possesses only the finite number of energy gaps is obtained. Using this result
the solution of the Korteveg–de Vries equation with the “finite-gap” initial condition
is expressed, by means of the $N$-dimensional $\Theta$-function, $N$ being the number of
the nondegenerate energy gaps. The following characteristic property of the $N$-gap
periodic potentials and the $N$-soliton decreasing potentials is discovered: the existence
of two solutions $\psi_1(x,\lambda), \psi_2(x,\lambda)$ of the Schrodinger equation, for which the product $\psi_1,\psi_2$ is the polynomial $P$ ($\operatorname{deg}P=N$. $N$ is the number of gaps or the number of bound states of $H$) from the spectral parameter $\lambda$.
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Theoretical and Mathematical Physics, 1975, 23:1, 343–355
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Received: 09.07.1974
Citation:
A. R. Its, V. B. Matveev, “Schrödinger operators with finite-gap spectrum and $N$-soliton solutions of the Korteweg–de Vries equation”, TMF, 23:1 (1975), 51–68; Theoret. and Math. Phys., 23:1 (1975), 343–355
Citation in format AMSBIB
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\by A.~R.~Its, V.~B.~Matveev
\paper Schr\"odinger operators with finite-gap spectrum and $N$-soliton solutions of the Korteweg--de~Vries equation
\jour TMF
\yr 1975
\vol 23
\issue 1
\pages 51--68
\mathnet{http://mi.mathnet.ru/tmf3750}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=479120}
\transl
\jour Theoret. and Math. Phys.
\yr 1975
\vol 23
\issue 1
\pages 343--355
\crossref{https://doi.org/10.1007/BF01038218}
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http://mi.mathnet.ru/eng/tmf3750 http://mi.mathnet.ru/eng/tmf/v23/i1/p51
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