Edit Profile Pogrebkov, Andrei K. Compute Distance To: Compute Author ID: pogrebkov.andrei-k Published as: Pogrebkov, A.; Pogrebkov, A. K.; Pogrebkov, Andrei; Pogrebkov, Andrei K. External Links: ORCID Documents Indexed: 86 Publications since 1978, including 1 Book all top 5 Co-Authors 23 single-authored 32 Boiti, Marco 32 Pempinelli, Flora 15 Polivanov, M. K. 13 Prinari, Barbara 12 Arkad’ev, V. A. 9 Polivanov, M. C. 5 Dzhordzhadze, G. P. 3 Garagash, T. I. 3 Kulaev, Ruslan Chermenovich 2 Martina, Luigi 2 Shabat, Alekseĭ Borisovich 1 Adler, Vsevolod Eduardovich 1 Askhabov, Sultan Nazhmudinovich 1 Beccaria, Matteo 1 Fokas, Athanassios S. 1 Konopelchenko, Boris Georgievich 1 Kusraev, Anatoly Georgievich 1 Kutateladze, Semën Samsonovich 1 Landolfi, Giulio 1 Mokhov, Oleg I. 1 Novikov, Sergeĭ Petrovich 1 Prati, M. C. 1 Reshetnyak, Yuriĭ Grigor’evich 1 Talalov, Sergeĭ Vladimirovich 1 Todorov, Ivan T. all top 5 Serials 27 Theoretical and Mathematical Physics 7 Inverse Problems 5 Journal of Mathematical Physics 4 Teoreticheskaya i Matematicheskaya Fizika 3 Soviet Physics. Doklady 2 Letters in Mathematical Physics 2 Russian Mathematical Surveys 2 Physica D 2 Journal of Physics A: Mathematical and General 2 Proceedings of the Steklov Institute of Mathematics 1 Nonlinearity 1 Physics Letters. A 1 Soviet Scientific Reviews. Section C 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 Journal of Soviet Mathematics 1 Acta Applicandae Mathematicae 1 Russian Mathematics 1 St. Petersburg Mathematical Journal 1 Journal of Nonlinear Mathematical Physics 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Journal of Physics A: Mathematical and Theoretical 1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 1 Symmetry all top 5 Fields 67 Partial differential equations (35-XX) 46 Dynamical systems and ergodic theory (37-XX) 19 Quantum theory (81-XX) 5 Ordinary differential equations (34-XX) 5 Difference and functional equations (39-XX) 5 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of particles and systems (70-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 1 Associative rings and algebras (16-XX) 1 Integral equations (45-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 68 Publications have been cited 356 times in 188 Documents Cited by ▼ Year ▼ Inverse scattering transform method and soliton solutions for Davey- Stewartson II equation. Zbl 0698.35150Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. C. 31 1989 Towards an inverse scattering theory for non-decaying potentials of the heat equation. Zbl 0988.35140Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 20 2001 Properties of solutions of the Kadomtsev-Petviashvili I equation. Zbl 0814.35116Boiti, M.; Pempinelli, F.; Pogrebkov, A. 16 1994 Inverse scattering transform for the KPI equation on the background of a one-line soliton. Zbl 1033.35097Fokas, A. S.; Pogrebkov, A. K. 15 2003 Solutions of the KPI equation with smooth initial data. Zbl 0806.35152Boiti, M.; Pempinelli, F.; Pogrebkov, A. 15 1994 Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation. Zbl 0806.35131Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C. 14 1992 Resolvent approach for the non-stationary Schrödinger equation. Zbl 0755.35109Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C. 14 1992 Inverse scattering theory of the heat equation for a perturbed one-soliton potential. Zbl 1059.35112Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 12 2002 Singular solutions of the equation (d’Alembert operator) \(\phi+(m^ 2/2)\exp \phi=0\) and dynamics of singularities. Zbl 0453.35058Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. K. 12 1980 Commutator identities on associative algebras and the integrability of nonlinear revolution equations. Zbl 1192.81191Pogrebkov, A. K. 9 2008 Singular solutions of the KdV equation and the inverse scattering method. Zbl 0571.35094Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 9 1984 The equivalence of different approaches for generating multisoliton solutions of the KPII equation. Zbl 1256.35112Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 7 2010 Building an extended resolvent of the heat operator via twisting transformations. Zbl 1176.35048Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 7 2009 Extended resolvent and inverse scattering with an application to KPI. Zbl 1062.37088Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 7 2003 The boson-fermion correspondence and quantum integrable and dispersionless models. Zbl 1063.81065Pogrebkov, A. K. 7 2003 The Liouville and Sinh-Gordon equations. Singular solutions, dynamics of singularities and the inverse problem method. Zbl 0604.70032Pogrebkov, A. K.; Polivanov, M. K. 7 1985 Singular solitons: An example of a sinh-Gordon equation. Zbl 0471.35057Pogrebkov, A. K. 7 1981 Hirota difference equation and a commutator identity on an associative algebra. Zbl 1222.37073Pogrebkov, A. K. 6 2011 On the extended resolvent of the nonstationary Schrödinger operator for a Darboux transformed potential. Zbl 1091.81015Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 6 2006 Solving the Kadomtsev-Petviashvili equation with initial data non vanishing at large distances. Zbl 0879.35133Boiti, M.; Pempinelli, F.; Pogrebkov, A. 6 1997 Some new methods and results in the theory of \((2+1)\)-dimensional integrable equations. Zbl 0850.35094Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 6 1994 New features of Bäcklund and Darboux transformations in \(2+1\) dimensions. Zbl 0726.58042Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C. 6 1991 Symmetries of the Hirota difference equation. Zbl 1372.35267Pogrebkov, Andrei K. 5 2017 Commutator identities on associative algebras, the non-abelian Hirota difference equation and its reductions. Zbl 1346.37056Pogrebkov, A. K. 5 2016 Heat operator with pure soliton potential: Properties of Jost and dual Jost solutions. Zbl 1272.35108Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 5 2011 2D Toda chain and associated commutator identity. Zbl 1151.37053Pogrebkov, A. K. 5 2008 Inverse scattering transform for the perturbed 1-soliton potential of the heat equation. Zbl 0969.35519Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 5 2001 Resolvent approach for the nonstationary Schrödinger equation (standard case of rapidly decreasing potential). Zbl 0941.35503Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C. 5 1992 Liouville field theory: IST and Poisson bracket structure. Zbl 0597.58044Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. C.; Talalov, S. V. 5 1986 Application of inverse scattering method to singular solutions of nonlinear equations. I. Zbl 0549.35106Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 5 1983 General solutions of the Cauchy problem for the Liouville equation \(\varphi_{tt}(t,x)-\varphi_{xx}(t,x)=(1/2)m \exp\varphi (t,x)\). Zbl 0417.35068Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. K. 5 1978 Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed \(N\)-soliton potential. Zbl 1112.37068Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 4 2006 Towards an inverse scattering theory for two-dimensional nondecaying potentials. Zbl 0951.35118Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 4 1998 Closed string-like solutions of the Davey-Stewartson equation. Zbl 0694.35143Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. C. 4 1989 Darboux system: Liouville reduction and an explicit solution. Zbl 1439.35401Kulaev, R. Ch.; Pogrebkov, A. K.; Shabat, A. B. 3 2018 Extended resolvent of the heat operator with a multisoliton potential. Zbl 1341.37034Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 3 2012 Scattering problem for the differential operator \(\partial_ x\partial_ y+1+a(x,y)\partial_ y+b(x+y)\). Zbl 0856.35096Garagash, T. I.; Pogrebkov, A. K. 3 1995 The KPI equation with unconstrained initial data. Zbl 0830.35113Boiti, M.; Pempinelli, F.; Pogrebkov, A. 3 1995 On the formulation of the Painlevé test as a criterion of complete integrability of partial differential equations. Zbl 0692.35141Pogrebkov, A. K. 3 1989 Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. II. Zbl 0717.34030Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 3 1988 Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. I. Zbl 0653.34017Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 3 1987 Singular solutions of the KdV equation and the inverse scattering method. Zbl 0599.35126Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 3 1985 Complete integrability of dynamical systems generated by singular solutions of Liouville’s equation. Zbl 0461.35083Pogrebkov, A. K. 3 1981 Cauchy-Jost function and hierarchy of integrable equations. Zbl 1339.37049Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 2 2015 Hirota difference equation: inverse scattering transform, Darboux transformation, and solitons. Zbl 1317.81252Pogrebkov, A. K. 2 2014 Spectral theory of the nonstationary Schrödinger equation with a two-dimensionally perturbed arbitrary one-dimensional potential. Zbl 1178.37096Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 2 2005 On time evolutions associated with the nonstationary Schrödinger equation. Zbl 0981.37027Pogrebkov, A. K. 2 2000 Dressing of a two-dimensional nontrivial potential. Zbl 1194.35398Boiti, M.; Pempinelli, F.; Pogrebkov, A. 2 1995 Closed string-like solutions of the Davey-Stewartson equation. Zbl 0728.35124Arkadiev, V. A.; Pogrebkov, A. K.; Polivanov, M. C. 2 1989 Expansion with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. I. Zbl 0633.34017Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 2 1987 Application of inverse scattering method to singular solutions of nonlinear equations. II. Zbl 0586.35075Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 2 1983 Higher Hirota difference equations and their reductions. Zbl 1429.39011Pogrebkov, A. K. 1 2018 Darboux system as three-dimensional analog of Liouville equation. Zbl 1412.35211Kulaev, R. Ch.; Pogrebkov, A. K.; Shabat, A. B. 1 2018 KPII: Cauchy-Jost function, Darboux transformations and totally nonnegative matrices. Zbl 1373.37155Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 1 2017 IST of KPII equation for perturbed multisoliton solutions. Zbl 1360.37164Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 1 2014 Hierarchy of quantum explicitly solvable and integrable models. Zbl 1330.81190Pogrebkov, A. K. 1 2006 Quantizing the KdV equation. Zbl 1038.81033Pogrebkov, A. K. 1 2001 Some nondecaying potentials for the heat conduction equation. Zbl 0966.35113Boiti, M.; Pempinelli, F.; Prinari, B.; Pogrebkov, A. K. 1 2000 Discrete Schrödinger equation on a finite field and associated cellular automaton. Zbl 0979.37033Pogrebkov, A. K. 1 1999 Bäcklund and Darboux transformations for the nonstationary Schrödinger equation. Zbl 1056.37511Boiti, M.; Pempinelli, F.; Pogrebkov, A.; Prinari, B. 1 1999 Spectral theory of solitons on a generic background for the KPI equation. Zbl 0941.35534Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 1 1996 Solution of the Cauchy problem for the Boiti-Leon-Pempinelli equation. Zbl 0941.35091Garagash, T. I.; Pogrebkov, A. K. 1 1996 Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. II. Zbl 0665.34026Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 1 1988 Liouville field theory. Zbl 0636.35079Pogrebkov, A. K.; Polivanov, M. K. 1 1988 Relativistic Hamiltonian dynamics of singularities of the Liouville equation. Zbl 0539.35068Pogrebkov, A. K.; Todorov, I. T. 1 1983 Nonlinear equations for fields radiated by particles. Zbl 0545.35059Pogrebkov, A. K. 1 1982 Global solution of the Liouville equation \(\phi_{tt} - \phi_{xx} + 1/2 \exp(\phi) = 0\) in a class of distributions. Zbl 0513.35051Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. K. 1 1981 Singular solutions of the equation \(\square\varphi +(m^2/2)\exp\varphi=O\) and the dynamics of singularities. Zbl 0415.35053Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. K. 1 1979 Darboux system: Liouville reduction and an explicit solution. Zbl 1439.35401Kulaev, R. Ch.; Pogrebkov, A. K.; Shabat, A. B. 3 2018 Higher Hirota difference equations and their reductions. Zbl 1429.39011Pogrebkov, A. K. 1 2018 Darboux system as three-dimensional analog of Liouville equation. Zbl 1412.35211Kulaev, R. Ch.; Pogrebkov, A. K.; Shabat, A. B. 1 2018 Symmetries of the Hirota difference equation. Zbl 1372.35267Pogrebkov, Andrei K. 5 2017 KPII: Cauchy-Jost function, Darboux transformations and totally nonnegative matrices. Zbl 1373.37155Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 1 2017 Commutator identities on associative algebras, the non-abelian Hirota difference equation and its reductions. Zbl 1346.37056Pogrebkov, A. K. 5 2016 Cauchy-Jost function and hierarchy of integrable equations. Zbl 1339.37049Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 2 2015 Hirota difference equation: inverse scattering transform, Darboux transformation, and solitons. Zbl 1317.81252Pogrebkov, A. K. 2 2014 IST of KPII equation for perturbed multisoliton solutions. Zbl 1360.37164Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 1 2014 Extended resolvent of the heat operator with a multisoliton potential. Zbl 1341.37034Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 3 2012 Hirota difference equation and a commutator identity on an associative algebra. Zbl 1222.37073Pogrebkov, A. K. 6 2011 Heat operator with pure soliton potential: Properties of Jost and dual Jost solutions. Zbl 1272.35108Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 5 2011 The equivalence of different approaches for generating multisoliton solutions of the KPII equation. Zbl 1256.35112Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 7 2010 Building an extended resolvent of the heat operator via twisting transformations. Zbl 1176.35048Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 7 2009 Commutator identities on associative algebras and the integrability of nonlinear revolution equations. Zbl 1192.81191Pogrebkov, A. K. 9 2008 2D Toda chain and associated commutator identity. Zbl 1151.37053Pogrebkov, A. K. 5 2008 On the extended resolvent of the nonstationary Schrödinger operator for a Darboux transformed potential. Zbl 1091.81015Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 6 2006 Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed \(N\)-soliton potential. Zbl 1112.37068Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 4 2006 Hierarchy of quantum explicitly solvable and integrable models. Zbl 1330.81190Pogrebkov, A. K. 1 2006 Spectral theory of the nonstationary Schrödinger equation with a two-dimensionally perturbed arbitrary one-dimensional potential. Zbl 1178.37096Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 2 2005 Inverse scattering transform for the KPI equation on the background of a one-line soliton. Zbl 1033.35097Fokas, A. S.; Pogrebkov, A. K. 15 2003 Extended resolvent and inverse scattering with an application to KPI. Zbl 1062.37088Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 7 2003 The boson-fermion correspondence and quantum integrable and dispersionless models. Zbl 1063.81065Pogrebkov, A. K. 7 2003 Inverse scattering theory of the heat equation for a perturbed one-soliton potential. Zbl 1059.35112Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 12 2002 Towards an inverse scattering theory for non-decaying potentials of the heat equation. Zbl 0988.35140Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 20 2001 Inverse scattering transform for the perturbed 1-soliton potential of the heat equation. Zbl 0969.35519Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 5 2001 Quantizing the KdV equation. Zbl 1038.81033Pogrebkov, A. K. 1 2001 On time evolutions associated with the nonstationary Schrödinger equation. Zbl 0981.37027Pogrebkov, A. K. 2 2000 Some nondecaying potentials for the heat conduction equation. Zbl 0966.35113Boiti, M.; Pempinelli, F.; Prinari, B.; Pogrebkov, A. K. 1 2000 Discrete Schrödinger equation on a finite field and associated cellular automaton. Zbl 0979.37033Pogrebkov, A. K. 1 1999 Bäcklund and Darboux transformations for the nonstationary Schrödinger equation. Zbl 1056.37511Boiti, M.; Pempinelli, F.; Pogrebkov, A.; Prinari, B. 1 1999 Towards an inverse scattering theory for two-dimensional nondecaying potentials. Zbl 0951.35118Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B. 4 1998 Solving the Kadomtsev-Petviashvili equation with initial data non vanishing at large distances. Zbl 0879.35133Boiti, M.; Pempinelli, F.; Pogrebkov, A. 6 1997 Spectral theory of solitons on a generic background for the KPI equation. Zbl 0941.35534Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 1 1996 Solution of the Cauchy problem for the Boiti-Leon-Pempinelli equation. Zbl 0941.35091Garagash, T. I.; Pogrebkov, A. K. 1 1996 Scattering problem for the differential operator \(\partial_ x\partial_ y+1+a(x,y)\partial_ y+b(x+y)\). Zbl 0856.35096Garagash, T. I.; Pogrebkov, A. K. 3 1995 The KPI equation with unconstrained initial data. Zbl 0830.35113Boiti, M.; Pempinelli, F.; Pogrebkov, A. 3 1995 Dressing of a two-dimensional nontrivial potential. Zbl 1194.35398Boiti, M.; Pempinelli, F.; Pogrebkov, A. 2 1995 Properties of solutions of the Kadomtsev-Petviashvili I equation. Zbl 0814.35116Boiti, M.; Pempinelli, F.; Pogrebkov, A. 16 1994 Solutions of the KPI equation with smooth initial data. Zbl 0806.35152Boiti, M.; Pempinelli, F.; Pogrebkov, A. 15 1994 Some new methods and results in the theory of \((2+1)\)-dimensional integrable equations. Zbl 0850.35094Boiti, M.; Pempinelli, F.; Pogrebkov, A. K. 6 1994 Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation. Zbl 0806.35131Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C. 14 1992 Resolvent approach for the non-stationary Schrödinger equation. Zbl 0755.35109Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C. 14 1992 Resolvent approach for the nonstationary Schrödinger equation (standard case of rapidly decreasing potential). Zbl 0941.35503Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C. 5 1992 New features of Bäcklund and Darboux transformations in \(2+1\) dimensions. Zbl 0726.58042Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C. 6 1991 Inverse scattering transform method and soliton solutions for Davey- Stewartson II equation. Zbl 0698.35150Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. C. 31 1989 Closed string-like solutions of the Davey-Stewartson equation. Zbl 0694.35143Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. C. 4 1989 On the formulation of the Painlevé test as a criterion of complete integrability of partial differential equations. Zbl 0692.35141Pogrebkov, A. K. 3 1989 Closed string-like solutions of the Davey-Stewartson equation. Zbl 0728.35124Arkadiev, V. A.; Pogrebkov, A. K.; Polivanov, M. C. 2 1989 Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. II. Zbl 0717.34030Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 3 1988 Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. II. Zbl 0665.34026Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 1 1988 Liouville field theory. Zbl 0636.35079Pogrebkov, A. K.; Polivanov, M. K. 1 1988 Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. I. Zbl 0653.34017Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 3 1987 Expansion with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. I. Zbl 0633.34017Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 2 1987 Liouville field theory: IST and Poisson bracket structure. Zbl 0597.58044Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. C.; Talalov, S. V. 5 1986 The Liouville and Sinh-Gordon equations. Singular solutions, dynamics of singularities and the inverse problem method. Zbl 0604.70032Pogrebkov, A. K.; Polivanov, M. K. 7 1985 Singular solutions of the KdV equation and the inverse scattering method. Zbl 0599.35126Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 3 1985 Singular solutions of the KdV equation and the inverse scattering method. Zbl 0571.35094Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 9 1984 Application of inverse scattering method to singular solutions of nonlinear equations. I. Zbl 0549.35106Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 5 1983 Application of inverse scattering method to singular solutions of nonlinear equations. II. Zbl 0586.35075Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. 2 1983 Relativistic Hamiltonian dynamics of singularities of the Liouville equation. Zbl 0539.35068Pogrebkov, A. K.; Todorov, I. T. 1 1983 Nonlinear equations for fields radiated by particles. Zbl 0545.35059Pogrebkov, A. K. 1 1982 Singular solitons: An example of a sinh-Gordon equation. Zbl 0471.35057Pogrebkov, A. K. 7 1981 Complete integrability of dynamical systems generated by singular solutions of Liouville’s equation. Zbl 0461.35083Pogrebkov, A. K. 3 1981 Global solution of the Liouville equation \(\phi_{tt} - \phi_{xx} + 1/2 \exp(\phi) = 0\) in a class of distributions. Zbl 0513.35051Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. K. 1 1981 Singular solutions of the equation (d’Alembert operator) \(\phi+(m^ 2/2)\exp \phi=0\) and dynamics of singularities. Zbl 0453.35058Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. K. 12 1980 Singular solutions of the equation \(\square\varphi +(m^2/2)\exp\varphi=O\) and the dynamics of singularities. Zbl 0415.35053Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. K. 1 1979 General solutions of the Cauchy problem for the Liouville equation \(\varphi_{tt}(t,x)-\varphi_{xx}(t,x)=(1/2)m \exp\varphi (t,x)\). Zbl 0417.35068Dzhordzhadze, G. P.; Pogrebkov, A. K.; Polivanov, M. K. 5 1978 all cited Publications top 5 cited Publications all top 5 Cited by 218 Authors 33 Pogrebkov, Andrei K. 14 Boiti, Marco 14 Pempinelli, Flora 9 Grinevich, Pëtr Georgievich 7 Klein, Christian 7 Saut, Jean-Claude 6 He, Jingsong 6 Prinari, Barbara 6 Talalov, Sergeĭ Vladimirovich 4 Fokas, Athanassios S. 4 Garagash, T. I. 4 Khabibullin, Ismagil Talgatovich 4 Prada, Julia 3 Abenda, Simonetta 3 Biondini, Gino 3 Cheng, Yi 3 Estévez, Pilar G. 3 Gil’, Michael Iosif 3 Kiselev, Oleg Mikhaĭlovich 3 Kulaev, Ruslan Chermenovich 3 Rao, Jiguang 3 Sakhnovich, Alexander L. 3 Santini, Paolo Maria 3 Shabat, Alekseĭ Borisovich 3 Villarroel, Javier 2 Ablowitz, Mark Jay 2 Arkad’ev, V. A. 2 Chakravarty, Sarbarish 2 Dai, Zhengde 2 de Alfaro, Vittorio 2 Dubrovin, Boris Anatol’evich 2 Filippov, Alexandre Tikhonovich 2 Fritzsche, Bernd 2 Gadyl’shin, Rustem R. 2 Grava, Tamara 2 Kaljakin, Leonid A. 2 Kalyakin, Leonid Anatol’evich 2 Kirstein, Bernd 2 Kiselev, O. M. 2 Koroteev, Peter 2 Kuznetsova, Mariya Nikolaevna 2 Ma, Wen-Xiu 2 Maruno, Kenichi 2 Molinet, Luc 2 Novikov, Sergeĭ Petrovich 2 Pokhozhaev, Stanislav I. 2 Polivanov, M. K. 2 Poptsova, Mariya Nikolaevna 2 Porsezian, Kuppusamy 2 Samoĭlenko, Yuliya Ivanivna 2 Samoĭlenko, Valeriĭ Grygorovych 2 Sciarappa, Antonio 2 Tzvetkov, Nikolay 2 Yurov, Artyom V. 2 Zarmi, Yair 2 Zharinov, Victor Victorovich 1 Adomian, George 1 Amor, Hédri Ben 1 Babaoglu, Ceni 1 Balog, János 1 Belokurov, Vladimir Viktorovich 1 Besse, Christophe 1 Beutler, Roland 1 Bica, Ion 1 Borisov, Alexander B. 1 Brown, Russell Murray 1 Bukhshtaber, Viktor Matveevich 1 Carroll, Robert L. 1 Cerveró, José M. 1 Chen, Yong 1 Clarkson, Peter A. 1 Constantin, Adrian 1 Cui, Shangbin 1 Ding, Qing 1 Dobrokhotov, Sergei Yurievich 1 Du, Yukun 1 Dubrovsky, V. G. 1 Dzhokhadze, Otar Mikhajlovich 1 Eden, Alp 1 Fehér, László M. 1 Finkel, Federico 1 Fuchssteiner, Benno 1 Gaillard, Pierre 1 Gao, Yali 1 Gavrylenko, Pavlo 1 Gerdzhikov, Vladimir Stefanov 1 Gesztesy, Fritz 1 Ghidaglia, Jean-Michel 1 Glutsyuk, Alexey A. 1 González-López, Artemio 1 Gorodtsov, Valentin A. 1 Guil, Francisco 1 Guo, Cuihua 1 Gürel, T. Burak 1 Han, Bo 1 Hoefer, Mark A. 1 Horowitz, Shai 1 Ivanov, Rossen I. 1 Jackiw, Roman W. 1 Jorjadze, George ...and 118 more Authors all top 5 Cited in 61 Serials 52 Theoretical and Mathematical Physics 19 Journal of Mathematical Physics 7 Studies in Applied Mathematics 6 Letters in Mathematical Physics 6 Physica D 4 Applicable Analysis 4 Communications in Mathematical Physics 4 Journal of Nonlinear Science 4 Journal of Nonlinear Mathematical Physics 3 Mathematical Notes 3 Nonlinearity 3 Applied Mathematics and Computation 3 Journal of Soviet Mathematics 3 Acta Applicandae Mathematicae 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 International Journal of Modern Physics A 2 Physics Letters. A 2 Ukrainian Mathematical Journal 2 Chaos, Solitons and Fractals 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Transactions of the American Mathematical Society 2 Applied Mathematics Letters 2 Russian Mathematics 2 Nonlinear Dynamics 2 Communications in Nonlinear Science and Numerical Simulation 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Proceedings of the Steklov Institute of Mathematics 2 Journal of Physics A: Mathematical and Theoretical 2 Ufimskiĭ Matematicheskiĭ Zhurnal 1 General Relativity and Gravitation 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Journal of Geometry and Physics 1 Prikladnaya Matematika i Mekhanika 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 Functional Analysis and its Applications 1 Journal of Differential Equations 1 Mathematics and Computers in Simulation 1 Proceedings of the American Mathematical Society 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Acta Mathematicae Applicatae Sinica. English Series 1 Linear Algebra and its Applications 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Selecta Mathematica. New Series 1 Bulletin des Sciences Mathématiques 1 Abstract and Applied Analysis 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Annales Henri Poincaré 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Differential Equations 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Asian-European Journal of Mathematics 1 Advances in Mathematical Physics 1 Annals of Functional Analysis 1 Symmetry all top 5 Cited in 33 Fields 135 Partial differential equations (35-XX) 92 Dynamical systems and ergodic theory (37-XX) 36 Quantum theory (81-XX) 11 Fluid mechanics (76-XX) 10 Ordinary differential equations (34-XX) 10 Difference and functional equations (39-XX) 8 Operator theory (47-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Numerical analysis (65-XX) 7 Algebraic geometry (14-XX) 7 Differential geometry (53-XX) 7 Relativity and gravitational theory (83-XX) 6 Nonassociative rings and algebras (17-XX) 3 Special functions (33-XX) 3 Mechanics of particles and systems (70-XX) 3 Mechanics of deformable solids (74-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year