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P.G.Grinevich: List of publications
1. Grinevich P.G. Rational solutions for the equations of commutation of differential
operators. --- Funct. Anal. i ego Pril., 1982, v.16, No 1, pp. 19­24 (in russian);
English translation: Funct. Anal. Appl., 1982, v. 16, pp. 15­19.
2. Novikov S.P., Grinevich P.G. About the spectral theory of commuting operators of
rank 2 with periodic coefficients. --- Funct. Anal. i ego Pril., 1982, v. 16, No 1, pp.
25­26 (in russian); English translation: Funct. Anal. Appl., 1982, v. 16, pp. 19­21.
3. Grinevich P.G. Commuting matrix differential orerators of arbitrary rank. --- Dokl.
Akad. Nauk SSSR, 1984, v.278, No 5, pp. 1048­1052. English translation: Soviet
Math. Dokl. 1984, v.30, No 2, pp. 515­518.
4. Grinevich P.G., Novikov R.G. Analogues of multisoliton potentials for the two­
dimensional Schrodinger operator. --- Funct. Anal. i ego Pril., 1985, v. 19, No 4,
pp. 32­42 (in russian); English translation: Funct.Anal.Appl., 1985, v.19, pp. 276­
285.
5. Grinevich P.G., Novikov R.G. Analogues of multisoliton potentials for the two­
dimensional Schrodinger operator, and a nonlocal Riemann problem. --- Dokl.
Akad. Nauk SSSR, 1986, v.286, No 1, pp. 19­22 (in russian). English transla­
tion: Soviet Math. Dokl. 1986, v.33, No 1, pp. 9­12.
6. Grinevich P.G. Manakov S.V. Inverse scattering problem for the two­dimensional
Schrodinger operator, ¯
@ ­ method and nonlinear equations. --- Funct. Anal. i ego
Pril., 1986, v. 20, No 1, pp. 14­24 (in russian); English translation: Funct. Anal.
Appl., 1986, v.20, pp. 94­103.
7. Grinevich P.G. Vector rank of commuting matrix differential operators. Proof of
the S.P.Novikov criterion. --- Izvestiia. AN SSSR, 1986, v.50, No 3, pp. 458­478 (in
russian); English translation: Mathematics of the USSR, Izvestiya, 1987, v. 28, No
3, pp. 445­465.
8. Grinevich P.G. Rational solitons of the Veselov­Novikov equations are potential
reflectionless at fixed energy. --- Teoreticheskaya i Mathematicheskaya Fizika, 1986,
v.69, No 2, pp. 307­310 (in russian); English translation: Theor. Math. Phys. 1986,
v.69, pp. 1170­1172.
9. Grinevich P.G., Novikov S.P. Two­dimensional ``inverse scattering problem'' for neg­
ative energies and generalized­analytic functions. 1. Energies below the ground
state. --- Funct. Anal. i ego Pril., 1988, v. 22, No 1, pp. 23­33 (in russian);
Funct.Anal.Appl., 1988, v. 22, pp. 19­27.
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10. Grinevich P.G., Volovik G.E. Topology of gap nodes in superfluid 3 He: ú 4
homotopy
group for 3 He \Gamma B disclination. --- Journal of Low Temp. Phys. 1988, v.72, Nos
5/6, 371­380.
11. Grinevich P.G., Novikov S.P. Two­dimensional ``inverse scattering problem'' for fixed
negative energies and generalized analytic functions. --- In Proc. of the ``Plasma
theory and nonlinear and turbulent processes in physics'' Workshop, Kiev 13­25
April 1987. World Scientific 1988, pp. 58­85.
12. Grinevich P.G., Novikov S.P. Inverse scattering problem for the two­dimensional
Schrodinger operator at a fixed negative energy and generalized analytic functions.
--- Proceedings of the 3 international workshop on nonlinear and turbulent processes
in physics.Kiev 13­26 April, 1987, Kiev, Naukova Dumka 1988, pp. 86­89.
13. Grinevich P.G. Fast decreasing potentials on a background of finite­zone potential
and the ¯
@ ­ problem on Riemann spaces. --- Funct. Anal. i ego Pril., 1989, v. 23,
No 4, pp. 79­80 (in russian); English translation: Funct. Anal. Appl. 1989, v. 23,
pp. 321­322.
14. Grinevich P.G., Orlov A.Yu. Vector fields action on Riemann surfaces and KP
theory. The Krichever­Novikov problem. --- In Nonlinear world: Proceedings of the
4 international workshop on nonlinear and turbulent processes in physics.Kiev 9­22
Oktober, 1989, Kiev, Naukova Dumka 1989, v. 2, pp.246­249.
15. Grinevich P.G., Orlov A.Yu. Wilson Ü ­ function and det ¯
@. --- In Nonlinear world:
Proceedings of the 4 international workshop on nonlinear and turbulent processes
in physics. Kiev 9­22 Oktober, 1989, Kiev, Naukova Dumka 1989,v. 2, pp.242­245.
16. Grinevich P.G., Orlov A.Yu. Virasoro action on Riemann surfaces, Grassmanians,
det ¯
@ and Segal­Wilson Ü ­ function.--- In Problems of modern quantum field theory
(Invited lecvtures of the spring school held in Alushta USSR, April 24 ­ May 5,
1989), ed. A.A.Belavin, A.U.Klimyk, A.B.Zamolodchikov, Springer­Verlag, 1989,
pp. 86­106.
17. Grinevich P.G., Orlov A.Yu. Variations of the complex structures of the Riemann
surfaces by the vector fields in the circle and the KP theory objects. The Krichever­
Novikov problem of the action on the Baker­Akhiezer function. --- Funct. Anal. i
ego Pril., 1990, v.24, No 1, pp. 72­73 (in russian); English translation: Funct. Anal.
Appl. 1990, v. 24, pp.61­64.
18. Grinevich P.G., Krichever I.M. Algebraic­geometry methods in soliton theory. ---
In ``Soliton theory: a survey of results'', ed. A.Fordy, University press, 1990, pp.
354­400.
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19. Grinevich P.G., Orlov A.Yu. Effect of additional symmetries of K­P equation on
the finite­gap solutions and variatons of Riemann surfaces. The Krichever­Novikov
problem. --- In ''Soliton and applications'' (Proceedings of the 4 international Work­
shop, Dubna, USSR, 24 ­ 26 August 1989), ed. V.G.Makhankov, V.K.Fedyanin,
O.K.Pashaev, World Scientific 1990, pp. 147­151.
20. Grinevich P.G., Orlov A.Yu. Higher (non­isospectral) symmetries of the Kadomtsev­
Petviashvily equations and the Virasoro action on Riemann surfsces. --- In ''Nonlin­
ear evolution equations and dinamical systems'', ed. S.Carillo, O.Ragnisco, Springer­
Verlag, 1990, pp 165­169.
21. Grinevich P.G., Orlov A.Yu. Virasoro algebra action on the moduli of Riemann sur­
faces. Realization in the Kadomtsev­Petviashvily equation theory. The Krichever­
Novikov problem about the action on the Baker­Akhieser function. --- In ``Geometry
and topology and applications'', Moscow, 1990 pp. 100­105, (in russian).
22. Benderskii V.A., Grinevich P.G., Makarov D.E., Pastur D.L. Preexponential factor
of rate constant of low­temperature chemical reactions. Fluctuational width of
tunneling channels and stability frequences. --- Chem. Phys., 1992, v.161, pp.
51­61.
23. Benderskii V.A., Grinevich P.G., Makarov D.E., Quantum chemical dinamics in two
dimensions. --- Chem. Phys., 1993, v. 170, pp. 275­293.
24. Grinevich P.G., Orlov A.Yu, Schulman E.I. On the symmetries of the integrable
systems. --- In the book. ``Important developments in soliton theory'', ed. A.
Fokas, V.E. Zakharov, Springer­Verlag, Berlin ­ Heidelberg ­ New York, 1993, pp.
283­301.
25. Grinevich P.G. The action of the Virasoro nonisospectral KdV symmetries of the
Whitham equations. ­ in ``Nonlinear Processes in Physics'' (Proccedings of the 3
Potsdam ­ 5 Kiev Workshop at Clarkson University, Potsdam, NY, USA, August
1­11, 1991), ed. A.S.Fokas, D.J.Kaup, A.C.Newell, V.E.Zakharov, Springer­Verlag,
1993, pp. 108­112.
26. Grinevich P.G., Novikov S.P. String equation­2. Physical solution. --- Algebra
and Analysis, 1994, v.6, No 3, pp. 118­140 (in russian); English translation: St.
Petersburg Math. J., 1995, v. 6, No 3, pp. 553­574; Avaliable in the electronic
preprint library: www.arxiv.org: solv­int/9501002.
27. P.G.Grinevich. Fast decaying potentials on the finite­gap background and the ¯
@­
problem on the Riemann surfaces. --- Teoreticheskaya i Mathematicheskaya Fizika,
1994, v. 99, No 2, pp. 300­308; Theor. Math. Phys., 1994, v.99, pp. 599­605.
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28. Grinevich P.G. Nonisospectral symmetries of the KdV equation and the correspond­
ing symmetries of the Whitham equations. --- In ``Singular limits of Dispersive
waves'', ed. N.M.Ercolany, I.R.Gabitov, C.D.Levermore, D.Serre, NATO ASI Se­
ries, Series B: Physics Vol. 320, Plenum, 1994, pp. 67­88. Avaliable in the electronic
preprint library: www.arxiv.org: solv­int/9509004.
29. Grinevich P.G., Schmidt M.U. Period preserving nonisospectral flows and the moduli
space of periodic solutions of soliton equations. --- Physica D, 1995, v. 87, pp 73­
98; SFB 288 preprint No 150, Berlin, Dec 1994; Avaliable in the electronic preprint
library: www.arxiv.org: solv­int/9412005.
30. Grinevich P.G., Novikov S.P.. Nonselfintersecting magnetic orbits on the plane.
Proof of Principle of the Overthrowing of the Cycles. ---Translations of American
Mathematical Society, series 2., 1995, v.170, pp. 199­206; Avaliable in the electronic
preprint library: www.arxiv.org: solv­int/9501006.
31. Grinevich P.G., Novikov R.G. Transparent Potentials at Fixed Energy in Dimension
Two. Fixed­Energy Dispersion Relations for the Fast Decaying Potentials. --- Com­
mun. Math. Phys., 1995, v.174, pp. 409­446; Avaliable in the electronic preprint
library: www.arxiv.org: solv­int/9410003.
32. Grinevich P.G., Schmidt M.U. Periodic preserving deformations of the finite­gap
solutions of the soliton equations. in: Proceedings of the first workshop ``Non­
linear physics. Theory and experiment''. editors: E.Alfinito, M.Boiti, L.Martina,
F.Pempinelli. World Scientific (1996). pp. 124­130.
33. Grinevich P.G. Nonsingularity of the direct scattering transform for the Kadomtsev­
Petviashvili 2 equation with real exponentially decaying at infinity potential. ---
Lett. Math. Phys., 1997, v. 40, pp. 59­73; Avaliable in the electronic preprint
library: www.arxiv.org: solv­int/9509010.
34. Grinevich P.G., Schmidt M.U. Closed curves in R 3 : a characterization in terms of
curvature and torsion, the Hasimoto map and periodic solutions of the Filament
Equation. --- SFB 288 preprint No 254; Avaliable in the electronic preprint library:
www.arxiv.org: dg­ga/9703020.
35. Grinevich P.G., Schmidt M.U. Conformal invariant functionals of immersions of tori
into R 3 ; --- Journal of Geometry and Physics, 1998, v. 26, No 1­2, pp. 51­78; SFB
288 preprint No 252, Berlin, Feb 1997; Avaliable in the electronic preprint library:
www.arxiv.org: dg­ga/9702015.
36. Grinevich P.G, Novikov R.G. Discrete spectrum for n­cell potentials. Rapport de
Recherche No 98/10­2, Universite de Nantes; Avaliable in the electronic preprint
library: www.arxiv.org: math­ph/9811014.
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37. Grinevich P.G. The scattering transform for the two­dimensional Schr¨odinger oper­
ator with a potential that decreases at infinity at fixed nonzero energy; --- Uspekhi
Mat. Nauk, 2000, v. 55, no. 6(336), pp. 3--70 (in russian); English translation:
Russian Math. Surveys, 2000, v. 55, no. 6, pp. 1015--1083.
38. Grinevich, P.G. Schmidt, M.U. Closed curves in R 3 and the nonlinear Schr¨odinger
equation. Proceedings of the Workshop on Nonlinearity, Integrability and All That:
Twenty Years after NEEDS '79 (Gallipoli, 1999), pp. 139--145, World Sci. Publish­
ing, River Edge, NJ, 2000.
39. Grinevich P.G. Approximation theorem for the self­focusing nonlinear Schr¨odinger
equation and for the periodic curves in R 3 . Advances in nonlinear mathematics
and science; --- Phys. D, 2001, v. 152/153, pp. 20--27. Avaliable in the electronic
preprint library: www.arxiv.org: nlin.si/0002020
40. Grinevich P.G., Novikov, S.P. Real finite­gap Sine­Gordon solutions: a formula for
topological charge; --- Uspekhi. Mat. Nauk, 2001, v. 56, no. 5, pp. 181--182
(russian); English translation: Russ. Math. Surveys, 2001, v. 56, no. 5, pp. 980--
981.
41. Grinevich P.G., Novikov S.P. Topological Charge of the real periodic finite­gap
Sine­Gordon solutions. To appear in: Comm. Pure Appl. Math. Avaliable in the
electronic preprint library: www.arxiv.org: math­ph/0111039.
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