Found 124 Documents (Results 1–100)

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Quasi-classical asymptotics of solutions to the matrix factorization problem with quadratically oscillating off-diagonal elements. (English. Russian original)Zbl 1307.35179

Funct. Anal. Appl. 48, No. 1, 1-14 (2014); translation from Funkts. Anal. Prilozh. 48, No. 1, 1-18 (2014).
MSC:  35Q15 35Q55 35B40
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A system of three three-dimensional charged quantum particles: asymptotic behavior of the eigenfunctions of the continuous spectrum at infinity. (English. Russian original)Zbl 1272.81185

Funct. Anal. Appl. 46, No. 2, 147-151 (2012); translation from Funkts. Anal. Prilozh. 46, No. 2, 83-88 (2012).
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Asymptotic behavior of eigenfunctions of the three-particle Schrödinger operator. II: Charged one-dimensional particles. (English. Russian original)Zbl 1219.81235

St. Petersbg. Math. J. 22, No. 3, 379-392 (2011); translation from Algebra Anal. 2010, No. 3, 60-79 (2010).
MSC:  81U10
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Homogenization in the scattering problem. (English. Russian original)Zbl 1271.35058

Funct. Anal. Appl. 44, No. 4, 243-252 (2010); translation from Funkts. Anal. Prilozh. 44, No. 4, 2-13 (2010).
MSC:  35P25
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Mikhail Shlemovich Birman (obituary). (English. Russian original)Zbl 1219.01025

Russ. Math. Surv. 65, No. 3, 569-575 (2010); translation from Uspekhi Mat. Nauk. 65, No. 3, 185-190 (2010).
MSC:  01A70
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The scattering matrix and associated formulas in Hamiltonian mechanics. (English)Zbl 1218.37072

MSC:  37J05 37J10 34L25 35P25 81U20
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New approach to numerical computation of the eigenfunctions of the continuous spectrum of three-particle Schrödinger operator. I: One-dimensional particles, short-range pair potentials. (English)Zbl 1193.81111

MSC:  81U10 34L25
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Uniform asymptotics of eigenfunctions for the three-body Schrödinger operator in one-dimensional case. (English)Zbl 1180.81132

Møller, Jacob S. (ed.) et al., Quantum few-body systems. Proceedings of the joint physics/mathematics workshop on quantum few-body systems, Aarhus, Denmark, 19–20 March 2007. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0517-2/hbk). AIP Conference Proceedings 998, 101-112 (2008).
MSC:  81U10 81Q05 70F07

Asymptotic behavior of the eigenfunctions of the many-particle Schrödinger operator. I: One-dimensional particles. (English)Zbl 1160.81476

Suslina, T. (ed.) et al., Spectral theory of differential operators. M. Sh. Birman 80th anniversary collection. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4738-1/hbk). Translations. Series 2. American Mathematical Society 225; Advances in the Mathematical Sciences 62, 55-71 (2008).
MSC:  81U10 81Q10

Linear adiabatic dynamics generated by operators with continuous spectrum. I. (English)Zbl 1152.35336

MSC:  35G10 35B40 35B25

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One-dimensional Schrödinger operator on the half-line: the differential equation for eigenfunctions with respect to the spectral parameter and an analog of the Freud equation. (English)Zbl 1168.34367

Funct. Anal. Appl. 41, No. 3, 237-240 (2007); translation from Funkts. Anal. Prilozh. 41, No. 3, 84-88 (2007).
MSC:  34L40 34L05
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Semiclassical pseudodifferential operators with discontinuous symbols and their applications to the problems of statistical physics. (English)Zbl 1142.35109

Birman, M. S. (ed.) et al., Nonlinear equations and spectral theory. Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4209-6/hbk). Translations. Series 2. American Mathematical Society 220. Advances in the Mathematical Sciences 59, 45-81 (2007).
MSC:  35S05 82B10 35B40

Remarks on the quantum adiabatic theorem. (English. Russian original)Zbl 1081.81040

St. Petersbg. Math. J. 16, No. 4, 639-648 (2005); translation from Algebra Anal. 16, No. 4, 41-53 (2004).
MSC:  81Q15 47N50
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Mikhail Shlemovich Birman (on the occasion of his 75th birthday). (English. Russian original)Zbl 1061.01500

St. Petersbg. Math. J. 16, No. 1, 1-8 (2004); translation from Algebra Anal. 16, No. 1, 5-14 (2004).
MSC:  01A70
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On asymptotic stability of solitary waves for nonlinear Schrödinger equations. (English)Zbl 1028.35139

MSC:  35Q55 37K40
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A class of the multi-interval eigenvalue distributions of matrix models and related structures. (English)Zbl 1041.81024

Malyshev, V. A. (ed.) et al., Asymptotic combinatorics with application to mathematical physics. Proceedings of the NATO Advanced Study Institute, St. Petersburg, Russia, July 9–22, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0792-2/hbk; 1-4020-0793-0/pbk). NATO Sci. Ser. II, Math. Phys. Chem. 77, 51-70 (2002).

Asymptotic stability of solitary waves for nonlinear Schrödinger equations. (English)Zbl 1017.35104

Bona, Jerry (ed.) et al., The legacy of the inverse scattering transform in applied mathematics. Proceedings of an AMS-IMS-SIAM joint summer research conference, South Hadley, MA, USA, June 17-21, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 301, 163-181 (2002).
MSC:  35Q55 37K45 35B40

On the difference equations with periodic coefficients. (English)Zbl 1012.39008

MSC:  39A11 39A12 37J45
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The Gel’fand-Levitan-Marchenko equation, and the long-time asymptotics of solutions of the nonlinear Schrödinger equation. (English. Russian original)Zbl 0998.35050

St. Petersbg. Math. J. 12, No. 5, 761-789 (2001); translation from Algebra Anal. 12, No. 5, 64-105 (2001).
MSC:  35Q55 35B40 47G30

Semiclassical pseudodifferential operators with double discontinuous symbols and their application to problems of quantum statistical physics. (English)Zbl 1136.35466

Demuth, Michael (ed.) et al., Partial differential equations and spectral theory. Proceedings of the PDE 2000 conference, Clausthal, Germany, July 24–28, 2000. Basel: Birkhäuser (ISBN 3-7643-6219-7/hbk). Oper. Theory, Adv. Appl. 126, 41-51 (2001).
MSC:  35S05 45P05 82B10

MSC:  35B10
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Simulation of instability of bright solitons for NLS with saturating nonlinearity. (English)Zbl 0972.78019

MSC:  78A60 35Q60
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The Gelfand-Levitan-Marchenko equation and the long-time asymptotics of the solutions of the nonlinear Schrödinger equation. (English)Zbl 0966.35121

Semenov-Tian-Shansky, Michael (ed.), L. D. Faddeev’s seminar on mathematical physics. Providence, RI: American Mathematical Society (AMS). Transl., Ser. 2, Am. Math. Soc. 201, 63-78 (2000).

Mikhail Shlyomovich Birman (on his 70th birthday). (English. Russian original)Zbl 0958.01026

Russ. Math. Surv. 55, No. 1, 201-205 (2000); translation from Usp. Mat. Nauk 55, No. 1, 204-207 (2000).
MSC:  01A70
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On the difference equations with periodic coefficients. (English)Zbl 1253.39002

De Wit, David (ed.) et al., 12th international congress of mathematical physics (ICMP’97). Proceedings of the congress held in Brisbane, Australia, July 13–19, 1997. Cambridge, MA: International Press (ISBN 1-57146-055-1). 303-308 (1999).
MSC:  39A10 39-02
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Kronig-Penney electron in a homogeneous electric field. (English)Zbl 0935.34072

Buslaev, V. (ed.) et al., Differential operators and spectral theory. M. Sh. Birman’s 70th anniversary collection. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 189(41), 45-57 (1999).
MSC:  34L40

On the scientific work of Mikhail Shlëmovich Birman. List of publications of M. Sh. Birman. (English)Zbl 1026.01503

Buslaev, V. (ed.) et al., Differential operators and spectral theory. M. Sh. Birman’s 70th anniversary collection. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 189(41), 1-15, 17-26 (1999).
MSC:  01A70

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Singularities of the Green function of the nonstationary Schrödinger equation. (English. Russian original)Zbl 0920.35008

Funct. Anal. Appl. 32, No. 2, 132-134 (1998); translation from Funkts. Anal. Prilozh. 32, No. 2, 80-83 (1998).
MSC:  35A20 81Q05
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The Harper equation: Monodromization without quasiclassics. (English. Russian original)Zbl 0866.34071

St. Petersbg. Math. J. 8, No. 2, 231-254 (1997); translation from Algebra Anal. 8, No. 2, 65-97 (1996).
MSC:  34L40 81Q05 34E20

The Harper equation: Monodromization without quasiclassics. (Russian)Zbl 0849.34066

MSC:  34L40 81Q05 34E20

Quasiclassical integral equations and the asymptotic behavior of solutions to the Korteweg-de Vries equation for large times. (English. Russian original)Zbl 0956.35114

Dokl. Math. 53, No. 3, 441-444 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 348, No. 4, 455-458 (1996).
MSC:  35Q53 37K15

Spectral properties of the monodromy matrix for Harper equation. (English)Zbl 0874.39006

MSC:  39A11 39A10
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Semiclassical integral equations on the semiaxis. (English)Zbl 0869.45003

Dobrushin, R. L. (ed.) et al., Topics in statistical and theoretical physics. F. A. Berezin memorial volume. Transl. ed. by A. B. Sossinsky. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 177(32), 45-49 (1996).
MSC:  45E10 45M05 47G10

Semiclassical asymptotics of the resolvent of the integral convolution operator with sine-kernel on a finite interval. (English. Russian original)Zbl 0862.35148

St. Petersbg. Math. J. 7, No. 6, 925-942 (1996); translation from Algebra Anal. 7, No. 6, 70-103 (1995).
MSC:  35S05 47G10

Bloch solutions for difference equations. (English. Russian original)Zbl 0859.39001

St. Petersbg. Math. J. 7, No. 4, 561-594 (1996); translation from Algebra Anal. 7, No. 4, 74-122 (1995).
MSC:  39A10 39A12 30D45

On the stability of solitary waves for nonlinear Schrödinger equations. (English)Zbl 0841.35108

Uraltseva, N. N. (ed.), Nonlinear evolution equations. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 164 (22), 75-98 (1995).
MSC:  35Q55 35Q51

Bloch solutions for difference equations. (Russian)Zbl 0847.39002

MSC:  39A10 39A12 30D45

The functional structure of the monodromy matrix for Harper’s equation. (English)Zbl 0816.34058

Demuth, Michael (ed.) et al., Mathematical results in quantum mechanics: International conference in Blossin (Germany), May 17-21, 1993. Basel: Birkhäuser Verlag. Oper. Theory, Adv. Appl. 70, 321-342 (1994).
MSC:  34L40 81Q05 34E20

The complex WKB method for Harper’s equation. I. (English. Russian original)Zbl 0839.34066

St. Petersbg. Math. J. 6, No. 3, 495-517 (1995); translation from Algebra Anal. 6, No. 3, 59-83 (1994).
MSC:  34E20

MSC:  34E20

Monodromization and the Harper equation. (English)Zbl 0880.34082

Reviewer: V.C.Boffi (Roma)
MSC:  34L05 34L40 34M99
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Equivalence of unstable anharmonic oscillators and double wells. (English)Zbl 0817.47077

MSC:  47N50 81Q10
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The trace formula for the nonlinear Klein-Gordon equation. (English)Zbl 0807.35132

Birman, M. Sh. (ed.), Wave propagation. Scattering theory. Transl. from the Russian by Peter Zhevandrov. Transl. ed. by Simeon Ivanov. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 157, 191-213 (1993).
MSC:  35Q55 70H03

Semiclassical integral equations with slowly decreasing kernels on finite domains. (English. Russian original)Zbl 0794.45001

St. Petersbg. Math. J. 5, No. 1, 141-158 (1994); translation from Algebra Anal. 5, No. 1, 160-178 (1993).
Reviewer: J.F.Toland (Bath)
MSC:  45A05 45M05 45E10

Nonlinear scattering: The states which are close to a soliton. (English. Russian original)Zbl 0836.35146

J. Math. Sci., New York 77, No. 3, 3161-3169 (1995); translation from Zap. Nauchn. Semi. POMI 200, 38-50 (1992).
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Scattering for the nonlinear Schrödinger equation: States close to a soliton. (English. Russian original)Zbl 0853.35112

St. Petersbg. Math. J. 4, No. 6, 1111-1142 (1993); translation from Algebra Anal. 4, No. 6, 63-102 (1992).
MSC:  35Q55 35P25 35B40

On nonlinear scattering of states which are close to a soliton. (English)Zbl 0795.35111

Robert, D. (ed.), Méthodes semi-classiques, Volume 2. Colloque international (Nantes, juin 1991). Paris: Société Mathématique de France, Astérisque. 210, 49-63 (1992).
MSC:  35Q55 35P25 35B40
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Nonlinear scattering: The states which are close to a soliton. (Russian. English summary)Zbl 0799.35197

Zap. Nauchn. Semin. POMI 200, 38-50, 70 (1992).
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Reflection operators and their applications to asymptotic investigations of semiclassical integral equations. (English)Zbl 0743.45003

Estimates and asymptotics for discrete spectra of integral and differential equations, Pap. Semin. Math. Phys., Leningrad/Russia 1989-90, Adv. Sov. Math. 7, 107-157 (1991).
MSC:  45A05 45M05 47A68

Optical and acoustic Fourier-processors. (English. Russian original)Zbl 0843.43012

Commutative harmonic analysis III. Encycl. Math. Sci. 72, 129-175 (1995); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 72, 135-180 (1991).
MSC:  43A99 78A40 94A12

Spectral properties of adiabatically perturbed differential operators with periodic coefficients. (English)Zbl 0726.34068

Recent developments in quantum mechanics, Proc. Conf., Braşov/Rom. 1989, Math. Phys. Stud. 12, 97-112 (1991).
MSC:  34L20

On spectral properties of adiabatically perturbed Schrödinger operators with periodic potentials. (English)Zbl 0739.35053

Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1990-1991, No.XXIII, 15 p. (1991).
MSC:  35P20 35Q55
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Quasiclassical integral equations. (English. Russian original)Zbl 0769.45009

Sov. Math., Dokl. 44, No. 1, 127-131 (1992); translation from Dokl. Akad. Nauk SSSR 319, No. 3, 527-530 (1991).
MSC:  45P05 45E10 45M05

A Bloch electron in an external field. (English. Russian original)Zbl 0726.34070

Leningr. Math. J. 1, No. 2, 287-320 (1990); translation from Algebra Anal. 1, No. 2, 1-29 (1989).
MSC:  34L25 81U30

Spectral properties of the operators $$H\psi =-\psi_{xx}+p(x)\psi +v(\epsilon x)\psi$$, p is periodic. (English)Zbl 0723.47042

Order, disorder and chaos in quantum systems, Proc. Conf., Dubna/USSR 1989, Oper. Theory, Adv. Appl. 46, 85-107 (1990).
MSC:  47F05 47A10

MSC:  81U10

Bloch electrons in an external electric field. (English)Zbl 0725.34097

Schrödinger operators, standard and non-standard, Proc. Conf., Dubna/USSR 1988, 103-129 (1989).
MSC:  34L40 81Q05

Bloch electron in an external field. (Russian)Zbl 0714.34128

Reviewer: W.Müller
MSC:  34L25 81U30

MSC:  81Q10

MSC:  01A70

Semiclassical approximation for equations with periodic coefficients. (English. Russian original)Zbl 0698.35130

Russ. Math. Surv. 42, No. 6, 97-125 (1987); translation from Usp. Mat. Nauk 42, No. 6, 77-98 (1987).
Reviewer: E.D.Belokolos
MSC:  35Q99 35G99 35B40
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MSC:  34E20

On the diffraction character of scattering in a quantum system of three one-dimensional particles. (English)Zbl 0616.47008

MSC:  47A40 81U10

On the asymptotic behavior of spectral characteristics of an integral operator with difference kernel on expanding regions. (English. Russian original)Zbl 0635.47006

Sov. Math., Dokl. 33, 400-403 (1986); translation from Dokl. Akad. Nauk SSSR, 287, 529-532 (1986).
Reviewer: L.Hacia
MSC:  47A10 47B38 47Gxx

Scattering theory for the Korteweg-de Vries (KdV) equation and its Hamiltonian interpretation. (English)Zbl 0618.35100

Reviewer: J.Kostarcuk
MSC:  35Q99 35A30 35P25
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Asymptotic behavior of solutions for t$$\to \infty$$ of the equation $$\psi _{xx}+u(x,t)\psi +(\lambda /4)\psi =0$$ with a potential u satisfying the Korteweg-de Vries equation. (Russian)Zbl 0606.35078

Reviewer: O.Dumbrajs

Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times. (English)Zbl 0597.35102

MSC:  35Q99 35B40
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Asymptotic behavior for t$$\to \infty$$ of the solutions of the equation $$\psi _{xx}+u(x,t)\psi +(\lambda /4)\psi =0$$ with a potential u, satisfying the Korteweg-de Vries equation. II. (English)Zbl 0582.35009

MSC:  35B40 35Q99 35J10
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On the asymptotic behavior as t$$\to \infty$$ of the solutions of the equation $$\psi _{xx}+u(x,t)\psi +(\lambda /4)\psi =0$$ with potential u satisfying the Korteweg-de Vries equation. I. (English)Zbl 0582.35008

MSC:  35B40 35Q99 34L99

Trace formula in Hamiltonian mechanics. (English)Zbl 0561.70016

MSC:  70H05 81Q05
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Regularization of many-particle scattering. (English)Zbl 0617.47006

Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, 1149-1159 (1984).
MSC:  47A40 81U10

Trace formula in Lagrangian mechanics. (English. Russian original)Zbl 0598.70023

Theor. Math. Phys. 61, 989-997 (1984); translation from Teor. Mat. Fiz. 61, No. 1, 52-63 (1984).
Reviewer: P.Smith
MSC:  70H03 37J99 49J15
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Trace formula in general Hamiltonian mechanics. (English. Russian original)Zbl 0598.70018

Theor. Math. Phys. 60, 863-871 (1984); translation from Teor. Mat. Fiz. 60, No. 3, 344-355 (1984).
Reviewer: N.Arley
MSC:  70H05 37J99
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On the asymptotic behaviour of solutions of the equation $$\psi _{xx}+u(x,t)\psi +(\lambda /4)\psi =0$$ with the potential u satisfying the Korteweg-de Vries equations, as t$$\to \infty$$. II. (Russian. English summary)Zbl 0559.35074

MSC:  35Q99 35J10 35B40
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MSC:  34E20
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MSC:  34E20

MSC:  76Q05
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Asymptotic methods in problems of the propagation of sound in oceanic waveguides and their numerical realization. (English)Zbl 0531.76089

MSC:  76Q05 86A05 76-02
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The trace formula in Hamiltonian mechanics. (Russian)Zbl 0537.70016

Reviewer: T.Atanacković
MSC:  70H05 81Q05
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On the asymptotic behaviour of solutions of the Korteweg-deVries equation for long times. (Russian)Zbl 0514.35077

MSC:  35Q99 35B40
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On the asymptotic behaviour for $$t\to \infty$$ of the solutions of the equation $$\psi_{xx} + u(x,t) \psi + (\lambda/4) \psi = 0$$ with a potential $$u$$ satisfying the Korteweg-deVries equation. I. (Russian)Zbl 0513.35011

MSC:  35B40 35Q99 34L99

Asymptotic methods in problems of sound propagation in ocean wave guides and their numerical realization. (Russian)Zbl 0482.76078

MSC:  76Q05 76-02 86A05
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MSC:  76Q05
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Variational calculus. Textbook. (Variatsionnoe ischislenie. Uchebnoe posobie). (Russian)Zbl 0489.49001

Leningradskij Ordena Lenina i Ordena Trudovogo Krasnogo Znameni Gosudarstvennyj Universitet im. A. A. Zhdanova. Leningrad: Izdatel’stvo Leningradskogo Universiteta. 288 p. R. 0.75 (1980).

On the diffraction characteristics of the scattering problem for a quantum system of three one-dimensional particles. (Russian)Zbl 0494.47010

MSC:  47A40 81U10

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A unitary regularizing operator for three-particle scattering. (Russian)Zbl 0498.35067

Partial differential equations, Proc. All-Union Conf., Moscow 1976, dedic. I. G. Petrovskij, 1606, 56-58 (1978).

Solutions of ”double soliton” type for the multidimensional equation d’Alembert operator(u)=F(u). (English)Zbl 0412.35061

MSC:  35L60 35C05
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The unitary regularization for a threeparticle scattering. (Russian)Zbl 0375.47005

MSC:  47A40 35P25 47F05

Solutions of the double soliton type for multidimensional equation $$\square u= F(u)$$. (Russian)Zbl 0346.35073

MSC:  35L60 35C05

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Trace formulas for multichannel problems. (English)Zbl 0349.47021

MSC:  47B10 46E35
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