Ramani, A.; Grammaticos, B.; Willox, R. Miura transformations for discrete Painlevé equations coming from the affine \(\operatorname{E}_{8}\) Weyl group. (English) Zbl 1365.39003 J. Math. Phys. 58, No. 4, 043502, 10 p. (2017). MSC: 39A12 34M55 37K35 PDF BibTeX XML Cite \textit{A. Ramani} et al., J. Math. Phys. 58, No. 4, 043502, 10 p. (2017; Zbl 1365.39003) Full Text: DOI arXiv
Kudryashov, Nikolay A. Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies. (English) Zbl 1328.35193 Regul. Chaotic Dyn. 19, No. 1, 48-63 (2014). MSC: 35Q51 35Q53 37K15 PDF BibTeX XML Cite \textit{N. A. Kudryashov}, Regul. Chaotic Dyn. 19, No. 1, 48--63 (2014; Zbl 1328.35193) Full Text: DOI
Rogers, Colin A novel Ermakov-Painlevé II system: \(N+1\)-dimensional coupled NLS and elastodynamic reductions. (English) Zbl 1297.35235 Stud. Appl. Math. 133, No. 2, 214-231 (2014). MSC: 35Q74 35Q53 34M55 PDF BibTeX XML Cite \textit{C. Rogers}, Stud. Appl. Math. 133, No. 2, 214--231 (2014; Zbl 1297.35235) Full Text: DOI
Novokshenov, V. Yu. Special solutions of the first and second Painlevé equations and singularities of the monodromy data manifold. (English. Russian original) Zbl 1301.34111 Proc. Steklov Inst. Math. 281, Suppl. 1, S105-S117 (2013); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 18, No. 2, 179-190 (2012). Reviewer: Tsvetana Stoyanova (Sofia) MSC: 34M55 34M35 PDF BibTeX XML Cite \textit{V. Yu. Novokshenov}, Proc. Steklov Inst. Math. 281, S105--S117 (2013; Zbl 1301.34111); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 18, No. 2, 179--190 (2012) Full Text: DOI
Kartak, V. V. Solution of the equivalence problem for the Painlevé IV equation. (English. Russian original) Zbl 1287.34079 Theor. Math. Phys. 173, No. 2, 1541-1564 (2012); translation from Teor. Mat. Fiz. 173, No. 2, 245-267 (2012). Reviewer: Tsvetana Stoyanova (Sofia) MSC: 34M55 PDF BibTeX XML Cite \textit{V. V. Kartak}, Theor. Math. Phys. 173, No. 2, 1541--1564 (2012; Zbl 1287.34079); translation from Teor. Mat. Fiz. 173, No. 2, 245--267 (2012) Full Text: DOI
Gontsov, R. R. On movable singularities of Garnier systems. (English. Russian original) Zbl 1232.34118 Math. Notes 88, No. 6, 806-818 (2010); translation from Mat. Zametki 88, No. 6, 845-858 (2010). Reviewer: Vladimir P. Kostov (Nice) MSC: 34M35 34M56 34M55 PDF BibTeX XML Cite \textit{R. R. Gontsov}, Math. Notes 88, No. 6, 806--818 (2010; Zbl 1232.34118); translation from Mat. Zametki 88, No. 6, 845--858 (2010) Full Text: DOI arXiv
Guha, Partha; Khanra, Barun; Choudhury, A. Ghose On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painlevé-Gambier type. (English) Zbl 1193.34074 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 7-8, 3247-3257 (2010). Reviewer: Oleg V. Makeev (Ulyanovsk) MSC: 34C14 34C20 34A05 PDF BibTeX XML Cite \textit{P. Guha} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 7--8, 3247--3257 (2010; Zbl 1193.34074) Full Text: DOI
Terzis, Petros A.; Christodoulakis, T. The general solution of Bianchi type VII\(_h\) vacuum cosmology. (English) Zbl 1182.83003 Gen. Relativ. Gravitation 41, No. 3, 469-495 (2009). Reviewer: Vojtěch Pravda (Praha) MSC: 83C15 83F05 PDF BibTeX XML Cite \textit{P. A. Terzis} and \textit{T. Christodoulakis}, Gen. Relativ. Gravitation 41, No. 3, 469--495 (2009; Zbl 1182.83003) Full Text: DOI
Kudryashov, Nikolai A.; Demina, Maria V. The generalized Yablonskii-Vorob’ev polynomials and their properties. (English) Zbl 1221.33033 Phys. Lett., A 372, No. 29, 4885-4890 (2008). MSC: 33E17 34M55 26C15 33E30 PDF BibTeX XML Cite \textit{N. A. Kudryashov} and \textit{M. V. Demina}, Phys. Lett., A 372, No. 29, 4885--4890 (2008; Zbl 1221.33033) Full Text: DOI
Kudryashov, Nikolai A. Special polynomials associated with some hierarchies. (English) Zbl 1220.34111 Phys. Lett., A 372, No. 12, 1945-1956 (2008). MSC: 34M55 33E17 34K07 PDF BibTeX XML Cite \textit{N. A. Kudryashov}, Phys. Lett., A 372, No. 12, 1945--1956 (2008; Zbl 1220.34111) Full Text: DOI
Tsegel’nik, V. V. Hamiltonians associated with the sixth Painlevé equation. (English. Russian original) Zbl 1189.35292 Theor. Math. Phys. 151, No. 1, 482-491 (2007); translation from Teor. Mat. Fiz. 151, No. 1, 54-65 (2007). MSC: 35Q53 37K05 37K35 35C11 PDF BibTeX XML Cite \textit{V. V. Tsegel'nik}, Theor. Math. Phys. 151, No. 1, 482--491 (2007; Zbl 1189.35292); translation from Teor. Mat. Fiz. 151, No. 1, 54--65 (2007) Full Text: DOI
Tamizhmani, K. M.; Ramani, A.; Tamizhmani, T.; Grammaticos, B. Special functions as solutions to discrete Painlevé equations. (English) Zbl 1107.39303 J. Comput. Appl. Math. 160, No. 1-2, 307-313 (2003). MSC: 39A12 33E17 34M55 37J35 PDF BibTeX XML Cite \textit{K. M. Tamizhmani} et al., J. Comput. Appl. Math. 160, No. 1--2, 307--313 (2003; Zbl 1107.39303) Full Text: DOI
Tamizhmani, T.; Grammaticos, B.; Tamizhmani, K. M.; Ramani, A. Special solutions of discrete Painlevé equations through direct linearisation. (English) Zbl 1001.34081 Physica A 315, No. 3-4, 569-582 (2002). MSC: 34M55 PDF BibTeX XML Cite \textit{T. Tamizhmani} et al., Physica A 315, No. 3--4, 569--582 (2002; Zbl 1001.34081) Full Text: DOI
Conte, Robert; Musette, Micheline New contiguity relation of the sixth Painlevé equation from a truncation. (English) Zbl 0996.34075 Physica D 161, No. 3-4, 129-141 (2002). Reviewer: Boris V.Loginov (Ulyanovsk) MSC: 34M55 PDF BibTeX XML Cite \textit{R. Conte} and \textit{M. Musette}, Physica D 161, No. 3--4, 129--141 (2002; Zbl 0996.34075) Full Text: DOI
Kudryashov, N. A.; Sukharev, M. B. Exact solutions of nonlinear fifth-order equation for describing waves in water. (English. Russian original) Zbl 1040.35072 J. Appl. Math. Mech. 65, No. 5, 855-865 (2001); translation from Prikl. Mat. Mekh. 65, No. 5, 884-894 (2001). Reviewer: A. Ja. Olejnik (Kyïv) MSC: 35Q35 35A99 PDF BibTeX XML Cite \textit{N. A. Kudryashov} and \textit{M. B. Sukharev}, Prikl. Mat. Mekh. 65, No. 5, 884--894 (2001; Zbl 1040.35072); translation from Prikl. Mat. Mekh. 65, No. 5, 884--894 (2001)
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M. Special function solutions of the discrete Painlevé equations. (English) Zbl 0994.33500 Comput. Math. Appl. 42, No. 3-5, 603-614 (2001). Reviewer: J.Saurer (Regensburg) MSC: 33E17 39A12 65Q05 PDF BibTeX XML Cite \textit{A. Ramani} et al., Comput. Math. Appl. 42, No. 3--5, 603--614 (2001; Zbl 0994.33500) Full Text: DOI
Ramani, A.; Carstea, A. S.; Grammaticos, B. Fermionic extensions of Painlevé equations. (English) Zbl 0988.81042 Phys. Lett., A 292, No. 1-2, 115-119 (2001). MSC: 81Q60 35Q53 37K35 34M55 33E17 37K10 PDF BibTeX XML Cite \textit{A. Ramani} et al., Phys. Lett., A 292, No. 1--2, 115--119 (2001; Zbl 0988.81042) Full Text: DOI
Tamizhmani, T.; Grammaticos, B.; Ramani, A.; Tamizhmani, K. M. On a class of special solutions of the Painlevé equations. (English) Zbl 0978.34080 Physica A 295, No. 3-4, 359-370 (2001). MSC: 34M55 PDF BibTeX XML Cite \textit{T. Tamizhmani} et al., Physica A 295, No. 3--4, 359--370 (2001; Zbl 0978.34080) Full Text: DOI
Kudryashov, Nikolai A. Double Bäcklund transformations and special integrals for the \(K_{II}\) hierarchy. (English) Zbl 1115.37355 Phys. Lett., A 273, No. 3, 194-202 (2000). MSC: 37K35 35A22 35Q58 37K10 PDF BibTeX XML Cite \textit{N. A. Kudryashov}, Phys. Lett., A 273, No. 3, 194--202 (2000; Zbl 1115.37355) Full Text: DOI
Grava, T. Existence of a global solution of the Whitham equations. (English. Russian original) Zbl 0997.37053 Theor. Math. Phys. 122, No. 1, 46-57 (2000); translation from Teor. Mat. Fiz. 122, No. 1, 58-71 (2000). Reviewer: Messoud Efendiev (Berlin) MSC: 37K10 35Q53 PDF BibTeX XML Cite \textit{T. Grava}, Theor. Math. Phys. 122, No. 1, 58--71 (2000; Zbl 0997.37053); translation from Teor. Mat. Fiz. 122, No. 1, 58--71 (2000) Full Text: DOI
Hinkkanen, Aimo; Laine, Ilpo Solutions of the first and second Painlevé equations are meromorphic. (English) Zbl 0986.34074 J. Anal. Math. 79, 345-377 (1999). Reviewer: Nikolay Vasilye Grigorenko (Kyïv) MSC: 34M55 34M05 PDF BibTeX XML Cite \textit{A. Hinkkanen} and \textit{I. Laine}, J. Anal. Math. 79, 345--377 (1999; Zbl 0986.34074) Full Text: DOI
Hone, Andrew N. W. Non-autonomous Hénon-Heiles systems. (English) Zbl 0937.37037 Physica D 118, No. 1-2, 1-16 (1998). MSC: 37K05 37N20 37K35 PDF BibTeX XML Cite \textit{A. N. W. Hone}, Physica D 118, No. 1--2, 1--16 (1998; Zbl 0937.37037) Full Text: DOI
Kudryashov, Nicolai A.; Soukharev, Mikhail B. Uniformization and transcendence of solutions for the first and second Painlevé hierarchies. (English) Zbl 0941.34077 Phys. Lett., A 237, No. 4-5, 206-216 (1998). MSC: 34M55 33E17 34A34 35Q53 37K10 34M05 PDF BibTeX XML Cite \textit{N. A. Kudryashov} and \textit{M. B. Soukharev}, Phys. Lett., A 237, No. 4--5, 206--216 (1998; Zbl 0941.34077) Full Text: DOI
Ramani, A.; Takahashi, D.; Grammaticos, B.; Ohta, Y. The ultimate discretisation of the Painlevé equations. (English) Zbl 0936.39006 Physica D 114, No. 3-4, 185-196 (1998). MSC: 39A12 37K35 PDF BibTeX XML Cite \textit{A. Ramani} et al., Physica D 114, No. 3--4, 185--196 (1998; Zbl 0936.39006) Full Text: DOI
Grammaticos, B.; Ohta, Y.; Ramani, A.; Takahashi, D.; Tamizhmani, K. M. Cellular automata and ultra-discrete Painlevé equations. (English) Zbl 0962.82527 Phys. Lett., A 226, No. 1-2, 53-58 (1997). MSC: 82C20 39A12 PDF BibTeX XML Cite \textit{B. Grammaticos} et al., Phys. Lett., A 226, No. 1--2, 53--58 (1997; Zbl 0962.82527) Full Text: DOI
Grammaticos, B.; Ohta, Y.; Ramani, A.; Takahashi, D.; Tamizhmani, K. M. Cellular automata and ultra-discrete Painlevé equations. (English) Zbl 0912.34005 Phys. Lett., A 226, No. 1-2, 53-58 (1997). MSC: 34A25 68Q80 34A26 34A34 PDF BibTeX XML Cite \textit{B. Grammaticos} et al., Phys. Lett., A 226, No. 1--2, 53--58 (1997; Zbl 0912.34005) Full Text: DOI
Tsegel’nik, V. V. On a relationship between solutions of the third Painlevé equation. (English. Russian original) Zbl 0856.35121 Theor. Math. Phys. 102, No. 3, 265-266 (1995); translation from Teor. Mat. Fiz. 102, No. 3, 364-366 (1995). MSC: 35Q58 58J72 PDF BibTeX XML Cite \textit{V. V. Tsegel'nik}, Theor. Math. Phys. 102, No. 3, 265--266 (1995; Zbl 0856.35121); translation from Teor. Mat. Fiz. 102, No. 3, 364--366 (1995) Full Text: DOI
Grammaticos, B.; Nijhoff, F. W.; Papageorgiou, V.; Ramani, A.; Satsuma, J. Linearization and solutions of the discrete Painlevé III equation. (English) Zbl 0941.34502 Phys. Lett., A 185, No. 5-6, 446-452 (1994). MSC: 34A34 34A05 PDF BibTeX XML Cite \textit{B. Grammaticos} et al., Phys. Lett., A 185, No. 5--6, 446--452 (1994; Zbl 0941.34502) Full Text: DOI
Adler, V. E. Nonlinear chains and Painlevé equations. (English) Zbl 0812.34030 Physica D 73, No. 4, 335-351 (1994). MSC: 34C20 34L40 34A25 PDF BibTeX XML Cite \textit{V. E. Adler}, Physica D 73, No. 4, 335--351 (1994; Zbl 0812.34030) Full Text: DOI
Grammaticos, B.; Nijhoff, F. W.; Papageorgiou, V.; Ramani, A.; Satsuma, J. Linearization and solutions of the discrete Painlevé III equation. (English) Zbl 0909.39004 Phys. Lett., A 185, No. 5-6, 446-452 (1994). MSC: 39A12 34B30 PDF BibTeX XML Cite \textit{B. Grammaticos} et al., Phys. Lett., A 185, No. 5--6, 446--452 (1994; Zbl 0909.39004) Full Text: DOI
Adler, V. E. Recuttings of polygons. (English. Russian original) Zbl 0812.58072 Funct. Anal. Appl. 27, No. 2, 141-143 (1993); translation from Funkts. Anal. Prilozh. 27, No. 2, 79-82 (1993). Reviewer: M.Farkas (Budapest) MSC: 37K35 PDF BibTeX XML Cite \textit{V. E. Adler}, Funct. Anal. Appl. 27, No. 2, 141--145 (1993; Zbl 0812.58072); translation from Funkts. Anal. Prilozh. 27, No. 2, 79--82 (1993) Full Text: DOI
Tamizhmani, K. M.; Grammaticos, B.; Ramani, A. Schlesinger transforms for the discrete Painlevé IV equation. (English) Zbl 0789.39001 Lett. Math. Phys. 29, No. 1, 49-54 (1993). Reviewer: L.Berg (Rostock) MSC: 39A10 37B99 58J72 PDF BibTeX XML Cite \textit{K. M. Tamizhmani} et al., Lett. Math. Phys. 29, No. 1, 49--54 (1993; Zbl 0789.39001) Full Text: DOI