Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O.; Sergyeyev, Artur Extended symmetry analysis of an isothermal no-slip drift flux model. (English) Zbl 1453.76186 Physica D 402, Article ID 132188, 16 p. (2020). MSC: 76M60 35B06 PDF BibTeX XML Cite \textit{S. Opanasenko} et al., Physica D 402, Article ID 132188, 16 p. (2020; Zbl 1453.76186) Full Text: DOI
Kulaev, R. Ch.; Shabat, A. B. Darboux system and separation of variables in the Goursat problem for a third order equation in \(\mathbb{R}^3\). (English. Russian original) Zbl 1445.37048 Russ. Math. 64, No. 4, 35-43 (2020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 4, 43-53 (2020). MSC: 37K25 37K30 PDF BibTeX XML Cite \textit{R. Ch. Kulaev} and \textit{A. B. Shabat}, Russ. Math. 64, No. 4, 35--43 (2020; Zbl 1445.37048); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 4, 43--53 (2020) Full Text: DOI
Khabirov, Salavat Valeevich Simple partially invariant solutions. (Russian. English summary) Zbl 07281232 Ufim. Mat. Zh. 11, No. 1, 87-98 (2019); translation in Ufa Math. J. 11, No. 1, 90-99 (2019). MSC: 35B35 35B06 PDF BibTeX XML Cite \textit{S. V. Khabirov}, Ufim. Mat. Zh. 11, No. 1, 87--98 (2019; Zbl 07281232); translation in Ufa Math. J. 11, No. 1, 90--99 (2019) Full Text: DOI MNR
Mokhov, O. I.; Pavlenko, N. A. Classification of the associativity equations with a first-order Hamiltonian operator. (English. Russian original) Zbl 1407.81098 Theor. Math. Phys. 197, No. 1, 1501-1513 (2018); translation from Teor. Mat. Fiz. 197, No. 1, 121-137 (2018). MSC: 81Q10 81T40 81T45 35Q35 PDF BibTeX XML Cite \textit{O. I. Mokhov} and \textit{N. A. Pavlenko}, Theor. Math. Phys. 197, No. 1, 1501--1513 (2018; Zbl 1407.81098); translation from Teor. Mat. Fiz. 197, No. 1, 121--137 (2018) Full Text: DOI
Pavlov, Maxim V.; Stoilov, Nikola M. The WDVV associativity equations as a high-frequency limit. (English) Zbl 1404.37077 J. Nonlinear Sci. 28, No. 5, 1843-1864 (2018). Reviewer: Ivan C. Sterling (St. Mary’s City) MSC: 37K05 37K10 37K20 37K25 PDF BibTeX XML Cite \textit{M. V. Pavlov} and \textit{N. M. Stoilov}, J. Nonlinear Sci. 28, No. 5, 1843--1864 (2018; Zbl 1404.37077) Full Text: DOI
Mokhov, Oleg I.; Strizhova, Nadezhda A. Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin-Novikov type. (English. Russian original) Zbl 1393.37071 Russ. Math. Surv. 73, No. 1, 175-177 (2018); translation from Usp. Mat. Nauk 73, No. 1, 183-184 (2018). MSC: 37K05 37K10 53D45 53B20 PDF BibTeX XML Cite \textit{O. I. Mokhov} and \textit{N. A. Strizhova}, Russ. Math. Surv. 73, No. 1, 175--177 (2018; Zbl 1393.37071); translation from Usp. Mat. Nauk 73, No. 1, 183--184 (2018) Full Text: DOI
Pavlov, M. V.; Vitolo, R. F. Remarks on the Lagrangian representation of bi-Hamiltonian equations. (English) Zbl 1358.37107 J. Geom. Phys. 113, 239-249 (2017). MSC: 37K05 37K10 37K20 37K25 PDF BibTeX XML Cite \textit{M. V. Pavlov} and \textit{R. F. Vitolo}, J. Geom. Phys. 113, 239--249 (2017; Zbl 1358.37107) Full Text: DOI arXiv
Zhuravlev, Victor M. Multidimensional quasilinear first-order equations and multivalued solutions of the elliptic and hyperbolic equations. (English. Russian original) Zbl 1338.35107 Theor. Math. Phys. 186, No. 3, 320-332 (2016); translation from Teor. Mat. Fiz. 186, No. 3, 371-385 (2016). MSC: 35F20 35G20 PDF BibTeX XML Cite \textit{V. M. Zhuravlev}, Theor. Math. Phys. 186, No. 3, 320--332 (2016; Zbl 1338.35107); translation from Teor. Mat. Fiz. 186, No. 3, 371--385 (2016) Full Text: DOI
Fedorov, V. E.; Davydov, P. N. On a class of generalized hydrodynamic type systems of equations. (English) Zbl 1323.35145 J. Appl. Nonlinear Dyn. 4, No. 3, 223-228 (2015). MSC: 35Q35 35G61 35A01 35A02 PDF BibTeX XML Cite \textit{V. E. Fedorov} and \textit{P. N. Davydov}, J. Appl. Nonlinear Dyn. 4, No. 3, 223--228 (2015; Zbl 1323.35145) Full Text: DOI
Pavlov, Maxim V.; Vitolo, Raffaele F. On the bi-Hamiltonian geometry of WDVV equations. (English) Zbl 1332.37048 Lett. Math. Phys. 105, No. 8, 1135-1163 (2015). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37K05 37K10 37K20 37K25 PDF BibTeX XML Cite \textit{M. V. Pavlov} and \textit{R. F. Vitolo}, Lett. Math. Phys. 105, No. 8, 1135--1163 (2015; Zbl 1332.37048) Full Text: DOI
Khabirov, S. V. Optimal system for the sum of two ideals admitted by the hydrodynamic type equations. (Russian. English summary) Zbl 1374.76189 Ufim. Mat. Zh. 6, No. 2, 94-103 (2014). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 76M60 35A30 35Q35 76N15 PDF BibTeX XML Cite \textit{S. V. Khabirov}, Ufim. Mat. Zh. 6, No. 2, 94--103 (2014; Zbl 1374.76189) Full Text: DOI
Arsie, Alessandro; Lorenzoni, Paolo \(F\)-manifolds with eventual identities, bidifferential calculus and twisted Lenard-Magri chains. (English) Zbl 1325.35156 Int. Math. Res. Not. 2013, No. 17, 3931-3976 (2013). Reviewer: Hsueh-Yung Lin (Palaiseau) MSC: 35Q35 37K25 53B15 53D45 PDF BibTeX XML Cite \textit{A. Arsie} and \textit{P. Lorenzoni}, Int. Math. Res. Not. 2013, No. 17, 3931--3976 (2013; Zbl 1325.35156) Full Text: DOI arXiv
Arsie, Alessandro; Lorenzoni, Paolo From the Darboux-Egorov system to bi-flat \(F\)-manifolds. (English) Zbl 1283.53077 J. Geom. Phys. 70, 98-116 (2013). MSC: 53D45 PDF BibTeX XML Cite \textit{A. Arsie} and \textit{P. Lorenzoni}, J. Geom. Phys. 70, 98--116 (2013; Zbl 1283.53077) Full Text: DOI arXiv
Rogers, C.; Schief, W. K. Connection of an integrable inhomogeneous Heisenberg spin equation to a hydrodynamic-type system with collision term. (English) Zbl 1253.82018 J. Phys. A, Math. Theor. 45, No. 43, Article ID 432002, 8 p. (2012). MSC: 82B20 76W05 PDF BibTeX XML Cite \textit{C. Rogers} and \textit{W. K. Schief}, J. Phys. A, Math. Theor. 45, No. 43, Article ID 432002, 8 p. (2012; Zbl 1253.82018) Full Text: DOI
Lorenzoni, Paolo; Pedroni, Marco; Raimondo, Andrea \(F\)-manifolds and integrable systems of hydrodynamic type. (English) Zbl 1249.35267 Arch. Math., Brno 47, No. 3, 163-180 (2011). Reviewer: Josef Šilhan (Brno) MSC: 35Q35 53B05 53D45 PDF BibTeX XML Cite \textit{P. Lorenzoni} et al., Arch. Math., Brno 47, No. 3, 163--180 (2011; Zbl 1249.35267) Full Text: EMIS EuDML arXiv
Ju, Qiuhong; Fu, Haiming; Dai, Zhengde Periodic-soliton wave solutions for \((2+1)\)-dimensional hydrodynamic-type system. (Chinese. English summary) Zbl 1240.35407 J. Zhoukou Norm. Univ. 27, No. 2, 1-4 (2010). MSC: 35Q35 35B10 35C08 PDF BibTeX XML Cite \textit{Q. Ju} et al., J. Zhoukou Norm. Univ. 27, No. 2, 1--4 (2010; Zbl 1240.35407)
Mokhov, O. I. Riemann invariants of semisimple non-locally bi-Hamiltonian systems of hydrodynamic type and compatible metrics. (English. Russian original) Zbl 1218.37092 Russ. Math. Surv. 65, No. 6, 1183-1185 (2010). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37K10 37K25 53B20 70G45 PDF BibTeX XML Cite \textit{O. I. Mokhov}, Russ. Math. Surv. 65, No. 6, 1183--1185 (2010; Zbl 1218.37092) Full Text: DOI
Odesskii, A. V.; Sokolov, V. V. Integrable elliptic pseudopotentials. (English. Russian original) Zbl 1180.37096 Theor. Math. Phys. 161, No. 1, 1340-1352 (2009); translation from Teor. Mat. Fiz. 161, No. 1, 21-36 (2009). MSC: 37K10 33C70 PDF BibTeX XML Cite \textit{A. V. Odesskii} and \textit{V. V. Sokolov}, Theor. Math. Phys. 161, No. 1, 1340--1352 (2009; Zbl 1180.37096); translation from Teor. Mat. Fiz. 161, No. 1, 21--36 (2009) Full Text: DOI
Conte, R.; Grundland, A. M.; Huard, B. Riemann-invariant solutions of the isentropic fluid flow equations. (English. Russian original) Zbl 1278.76098 Theor. Math. Phys. 159, No. 3, 752-762 (2009); translation from Teor. Mat. Fiz. 159, No. 3, 399-410 (2009). MSC: 76N10 35A30 35Q35 PDF BibTeX XML Cite \textit{R. Conte} et al., Theor. Math. Phys. 159, No. 3, 752--762 (2009; Zbl 1278.76098); translation from Teor. Mat. Fiz. 159, No. 3, 399--410 (2009) Full Text: DOI
Pavlov, Maxim V.; Popowicz, Ziemowit On integrability of a special class of two-component (2+1)-dimensional hydrodynamic-type systems. (English) Zbl 1160.37398 SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 011, 10 p. (2009). MSC: 37K10 35Q53 PDF BibTeX XML Cite \textit{M. V. Pavlov} and \textit{Z. Popowicz}, SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 011, 10 p. (2009; Zbl 1160.37398) Full Text: DOI EuDML
Odesskii, A. V.; Sokolov, V. V. On \((2+1)\)-dimensional hydrodynamic type systems possessing a pseudopotential with movable singularities. (English) Zbl 1175.35028 Funct. Anal. Appl. 42, No. 3, 205-212 (2008); translation from Funkts. Anal. Prilozh. 42, No. 3, 53-62 (2008). MSC: 35C05 37K10 76N10 PDF BibTeX XML Cite \textit{A. V. Odesskii} and \textit{V. V. Sokolov}, Funct. Anal. Appl. 42, No. 3, 205--212 (2008; Zbl 1175.35028); translation from Funkts. Anal. Prilozh. 42, No. 3, 53--62 (2008) Full Text: DOI
Odesskii, Alexander A family of \((2+1)\)-dimensional hydrodynamic type systems possessing a pseudopotential. (English) Zbl 1237.37048 Sel. Math., New Ser. 13, No. 4, 727-742 (2007). MSC: 37K10 35Q35 14H70 PDF BibTeX XML Cite \textit{A. Odesskii}, Sel. Math., New Ser. 13, No. 4, 727--742 (2007; Zbl 1237.37048) Full Text: DOI arXiv
Pavlov, M. V. Integrability of the egorov systems of hydrodynamic type. (English. Russian original) Zbl 1125.37049 Theor. Math. Phys. 150, No. 2, 225-243 (2007); translation from Teor. Mat. Fiz. 150, No. 2, 263-285 (2007). MSC: 37K10 37K05 37N10 35Q99 PDF BibTeX XML Cite \textit{M. V. Pavlov}, Theor. Math. Phys. 150, No. 2, 225--243 (2007; Zbl 1125.37049); translation from Teor. Mat. Fiz. 150, No. 2, 263--285 (2007) Full Text: DOI
Xue, Ting; Zhang, Youjin Bihamiltonian systems of hydrodynamic type and reciprocal transformations. (English) Zbl 1104.37051 Lett. Math. Phys. 75, No. 1, 79-92 (2006). MSC: 37N10 37K25 37K10 PDF BibTeX XML Cite \textit{T. Xue} and \textit{Y. Zhang}, Lett. Math. Phys. 75, No. 1, 79--92 (2006; Zbl 1104.37051) Full Text: DOI arXiv
Pavlov, M. V. The description of pairs of compatible first-order differential geometric Poisson brackets. (English) Zbl 1178.37066 Theor. Math. Phys. 142, No. 2, 244-258 (2005); translation from Teor. Mat. Fiz. 142, No. 2, 293-309 (2005). MSC: 37K05 53D17 37K10 PDF BibTeX XML Cite \textit{M. V. Pavlov}, Theor. Math. Phys. 142, No. 2, 244--258 (2005; Zbl 1178.37066); translation from Teor. Mat. Fiz. 142, No. 2, 293--309 (2005) Full Text: DOI
Mokhov, O. I. The Liouville canonical form for compatible nonlocal Poisson brackets of hydrodynamic type and integrable hierarchies. (English. Russian original) Zbl 1043.37049 Funct. Anal. Appl. 37, No. 2, 103-113 (2003); translation from Funkts. Anal. Prilozh. 37, No. 2, 28-40 (2003). MSC: 37K10 53C21 PDF BibTeX XML Cite \textit{O. I. Mokhov}, Funct. Anal. Appl. 37, No. 2, 103--113 (2003; Zbl 1043.37049); translation from Funkts. Anal. Prilozh. 37, No. 2, 28--40 (2003) Full Text: DOI
Ladyzhenskaya, O. A. On multiplicators in the Hölder spaces and exact solutions of hyperbolic type linear systems. (Russian) Zbl 1011.35032 Izv. Vyssh. Uchebn. Zaved., Sev.-Kavk. Reg., Estestv. Nauki 2000, No. 3, 88-90 (2000). Reviewer: Andrei Zemskov (Moskva) MSC: 35B45 26A16 PDF BibTeX XML Cite \textit{O. A. Ladyzhenskaya}, Izv. Vyssh. Uchebn. Zaved., Sev.-Kavk. Reg., Estestv. Nauki 2000, No. 3, 88--90 (2000; Zbl 1011.35032)
Miyaoka, Reiko On the theory of integrable systems and its applications. (English) Zbl 0963.53031 Suh, Young Jin (ed.), Proceedings of the third international workshop on differential geometry, Taegu, Korea, October 30-31, 1998. Taegu: Kyungpook National University, Basic Science Research Institute, 41-55 (1999). Reviewer: D.Ferus (Berlin) MSC: 53C40 37K25 PDF BibTeX XML Cite \textit{R. Miyaoka}, in: Proceedings of the third international workshop on differential geometry, Taegu, Korea, October 30--31, 1998. Taegu: Kyungpook National University, Basic Science Research Institute. 41--55 (1999; Zbl 0963.53031)
Fairlie, D. B.; Strachan, I. A. B. The Hamiltonian structure of the dispersionless Toda hierarchy. (English) Zbl 0885.35131 Physica D 90, No. 1-2, 1-8 (1996). MSC: 35Q58 37J35 37K10 PDF BibTeX XML Cite \textit{D. B. Fairlie} and \textit{I. A. B. Strachan}, Physica D 90, No. 1--2, 1--8 (1996; Zbl 0885.35131) Full Text: DOI
Galaktionov, E. V.; Zilberglejt, A. S. Attractors of hydrodynamic-type systems. (English) Zbl 0802.34065 Koptev, Yu. I. (ed.), Mathematical physics, applied mathematics and informatics. Commack, NY: Nova Science Publishers, Inc.. 231-266 (1993). Reviewer: N.Medvedeva (Chelyabinsk) MSC: 34D45 37D45 34-02 PDF BibTeX XML Cite \textit{E. V. Galaktionov} and \textit{A. S. Zilberglejt}, in: Mathematical physics, applied mathematics and informatics. Commack, NY: Nova Science Publishers, Inc.. 231--266 (1993; Zbl 0802.34065)
Novikov, S. P. Hydrodynamics of soliton lattices: Differential geometry and Hamiltonian formalism. (English) Zbl 0822.35114 Girardi, M. (ed.) et al., Progress in variational methods in Hamiltonian systems and elliptic equations. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 243, 144-156 (1992). Reviewer: J.Chrastina (Brno) MSC: 35Q51 37J99 39A12 PDF BibTeX XML Cite \textit{S. P. Novikov}, in: Progress in variational methods in Hamiltonian systems and elliptic equations. Harlow: Longman Scientific \& Technical; New York: Wiley. 144--156 (1992; Zbl 0822.35114)
Dubrovin, Boris A. Geometry of Hamiltonian evolutionary systems. (English) Zbl 0936.37022 Monographs and Textbooks in Physical Science. Lecture Notes. 22. Naples: Bibliopolis. iv, 131 p. (1991). Reviewer: V.Mikhalev (MR 93k:58112) MSC: 37Jxx 37Kxx 37-02 53-02 53D17 81R50 37J40 81Q20 37K10 37N20 PDF BibTeX XML Cite \textit{B. A. Dubrovin}, Geometry of Hamiltonian evolutionary systems. Naples: Bibliopolis (1991; Zbl 0936.37022)