Geodesic
On spectral curve for functional-difference Shr\"odinger equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 107-120

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The method of construction some set of finite-gap solutions of functional-difference deformation Shrödinger equation $v(x)f(x+2h)+f(x)=\lambda f(x+h)$ is offered. It is shown that edges of gaps of corresponding spectral curve depend on $x$. Examples are given. Bibl. – 7 titles. 
@article{ZNSL_2010_374_a6,
     author = {G. M. Golovachev and A. O. Smirnov},
     title = {On spectral curve for functional-difference {Shr\"odinger} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {107--120},
     publisher = {mathdoc},
     volume = {374},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a6/}
}
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G. M. Golovachev; A. O. Smirnov. On spectral curve for functional-difference Shr\"odinger equation. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 107-120. http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a6/