Class information for:
Level 1: PAINLEVE EQUATIONS//ISOMONODROMIC DEFORMATIONS//PAINLEVE HIERARCHY

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
9284 1170 21.9 38%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
10 4 OPTICS//PHYSICS, PARTICLES & FIELDS//PHYSICS, MULTIDISCIPLINARY 1131262
299 3       PHYSICS, MATHEMATICAL//JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS//BACKLUND TRANSFORMATION 41113
127 2             PHYSICS, MATHEMATICAL//BACKLUND TRANSFORMATION//SOLITON SOLUTION 23959
9284 1                   PAINLEVE EQUATIONS//ISOMONODROMIC DEFORMATIONS//PAINLEVE HIERARCHY 1170

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 PAINLEVE EQUATIONS authKW 1389590 9% 50% 106
2 ISOMONODROMIC DEFORMATIONS authKW 856313 4% 75% 44
3 PAINLEVE HIERARCHY authKW 365358 1% 100% 14
4 MIDDLE CONVOLUTION authKW 315026 1% 93% 13
5 FUCHSIAN SYSTEM authKW 279602 1% 71% 15
6 SCHLESINGER SYSTEM authKW 208776 1% 100% 8
7 GARNIER SYSTEM authKW 167018 1% 80% 8
8 PAINLEVE TRANSCENDENTS authKW 163378 1% 52% 12
9 MONODROMY DATA authKW 156582 1% 100% 6
10 THE PAINLEVE EQUATIONS authKW 156582 1% 100% 6

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Physics, Mathematical 17605 34% 0% 402
2 Mathematics 12827 45% 0% 531
3 Mathematics, Applied 4932 26% 0% 309
4 Physics, Multidisciplinary 1536 18% 0% 209
5 Multidisciplinary Sciences 203 2% 0% 29
6 Mathematics, Interdisciplinary Applications 25 2% 0% 18
7 Mechanics 7 2% 0% 23
8 Automation & Control Systems 3 1% 0% 9
9 Physics, Particles & Fields 2 1% 0% 17
10 Logic 0 0% 0% 1

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 EDIFICIO FIS 108736 0% 83% 5
2 SEKI KOWA MATH 78291 0% 100% 3
3 THEORY INFORMAT TRANSMISS CONTROL 52194 0% 100% 2
4 HBEREICH MATH AG 2 34795 0% 67% 2
5 AREA MATEMAT LICADA 30297 1% 19% 6
6 AREA FIS TEOR 28430 1% 8% 13
7 ANR SEDIGA 26097 0% 100% 1
8 AUSTRALIAN COUNCIL EXCELLENCE MATH ST 26097 0% 100% 1
9 AUSTRALIAN COUNCIL EXCELLENCE STAT COMPLEX 26097 0% 100% 1
10 CORSO DOTTORATO MATEMAT METODI PLICAZ 26097 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 BULLETIN DE LA CLASSE DES SCIENCES ACADEMIE ROYALE DE BELGIQUE 71339 2% 14% 19
2 FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA 36061 2% 7% 19
3 STUDIES IN APPLIED MATHEMATICS 25632 3% 3% 33
4 DIFFERENTIAL EQUATIONS 19586 5% 1% 53
5 PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 17565 3% 2% 39
6 JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS 7897 2% 2% 18
7 SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 7840 2% 2% 19
8 NAGOYA MATHEMATICAL JOURNAL 7749 2% 2% 19
9 THEORETICAL AND MATHEMATICAL PHYSICS 7066 3% 1% 37
10 NONLINEARITY 6710 2% 1% 29

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 PAINLEVE EQUATIONS 1389590 9% 50% 106 Search PAINLEVE+EQUATIONS Search PAINLEVE+EQUATIONS
2 ISOMONODROMIC DEFORMATIONS 856313 4% 75% 44 Search ISOMONODROMIC+DEFORMATIONS Search ISOMONODROMIC+DEFORMATIONS
3 PAINLEVE HIERARCHY 365358 1% 100% 14 Search PAINLEVE+HIERARCHY Search PAINLEVE+HIERARCHY
4 MIDDLE CONVOLUTION 315026 1% 93% 13 Search MIDDLE+CONVOLUTION Search MIDDLE+CONVOLUTION
5 FUCHSIAN SYSTEM 279602 1% 71% 15 Search FUCHSIAN+SYSTEM Search FUCHSIAN+SYSTEM
6 SCHLESINGER SYSTEM 208776 1% 100% 8 Search SCHLESINGER+SYSTEM Search SCHLESINGER+SYSTEM
7 GARNIER SYSTEM 167018 1% 80% 8 Search GARNIER+SYSTEM Search GARNIER+SYSTEM
8 PAINLEVE TRANSCENDENTS 163378 1% 52% 12 Search PAINLEVE+TRANSCENDENTS Search PAINLEVE+TRANSCENDENTS
9 MONODROMY DATA 156582 1% 100% 6 Search MONODROMY+DATA Search MONODROMY+DATA
10 THE PAINLEVE EQUATIONS 156582 1% 100% 6 Search THE+PAINLEVE+EQUATIONS Search THE+PAINLEVE+EQUATIONS

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 CLARKSON, PA , (2006) PAINLEVE EQUATIONS - NONLINEAR SPECIAL FUNCTIONS.ORTHOGONAL POLYNOMIALS AND SPECIAL FUNCTIONS: COMPUTATION AND APPLICATIONS. VOL. 1883. ISSUE . P. 331 -411 95 72% 16
2 FILIPUK, GV , CLARKSON, PA , (2008) THE SYMMETRIC FOURTH PAINLEVE HIERARCHY AND ASSOCIATED SPECIAL POLYNOMIALS.STUDIES IN APPLIED MATHEMATICS. VOL. 121. ISSUE 2. P. 157 -188 51 88% 9
3 GORDOA, PR , PICKERING, A , ZHU, ZN , (2016) ON MATRIX PAINLEVE HIERARCHIES.JOURNAL OF DIFFERENTIAL EQUATIONS. VOL. 261. ISSUE 2. P. 1128 -1175 35 74% 0
4 ANOSOV, DV , LEKSIN, VP , (2011) ANDREI ANDREEVICH BOLIBRUKH'S WORKS ON THE ANALYTIC THEORY OF DIFFERENTIAL EQUATIONS.RUSSIAN MATHEMATICAL SURVEYS. VOL. 66. ISSUE 1. P. 1 -33 26 100% 0
5 COSGROVE, CM , (2006) HIGHER-ORDER PAINLEVE EQUATIONS IN THE POLYNOMIAL CLASS II: BUREAU SYMBOL P1.STUDIES IN APPLIED MATHEMATICS. VOL. 116. ISSUE 4. P. 321 -413 35 78% 25
6 KUDRYASHOV, NA , (2014) HIGHER PAINLEVE TRANSCENDENTS AS SPECIAL SOLUTIONS OF SOME NONLINEAR INTEGRABLE HIERARCHIES.REGULAR & CHAOTIC DYNAMICS. VOL. 19. ISSUE 1. P. 48-63 30 75% 2
7 CLARKSON, PA , (2003) PAINLEVE' EQUATIONS - NONLINEAR SPECIAL FUNCTIONS.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. VOL. 153. ISSUE 1-2. P. 127 -140 39 74% 26
8 GORDOA, PR , MUGAN, U , PICKERING, A , SAKKA, A , (2004) BACKLUND TRANSFORMATIONS FOR HIGHER ORDER PAINLEVE EQUATIONS.CHAOS SOLITONS & FRACTALS. VOL. 22. ISSUE 5. P. 1103-1115 28 100% 3
9 GUZZETTI, D , (2015) A REVIEW OF THE SIXTH PAINLEV, EQUATION.CONSTRUCTIVE APPROXIMATION. VOL. 41. ISSUE 3. P. 495 -527 23 92% 0
10 BIBILO, Y , FILIPUK, G , (2015) NON-SCHLESINGER ISOMONODROMIC DEFORMATIONS OF FUCHSIAN SYSTEMS AND MIDDLE CONVOLUTION.SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. VOL. 11. ISSUE . P. - 20 95% 1

Classes with closest relation at Level 1


Rank Class id link
1 4250 GMPIB//IMNC//UMR 8165
2 16080 DIFFERENTIAL GALOIS THEORY//NON INTEGRABILITY//DIFFERENTIAL GALOIS GROUP
3 17494 BOREL SUMMABILITY//STOKES PHENOMENON//MULTISUMMABILITY
4 32719 POWER EXPONENTIAL FUNCTIONS//POWER INEQUALITIES//LIMIT FAMILIES
5 34768 ERGODIC INVARIANTS//ERGODIC PARAMETERS//GRADIENT HAMILTONIAN DECOMPOSITION
6 8784 FROBENIUS MANIFOLDS//WHITHAM EQUATIONS//HYDRODYNAMIC REDUCTIONS
7 18752 GLOBAL RELATION//RIEMANN HILBERT PROBLEM//RIEMANN HILBERT PROBLEMS
8 3500 RANDOM MATRICES//RANDOM MATRICES-THEORY AND APPLICATIONS//LIMITING SPECTRAL DISTRIBUTION
9 22938 SIGMA FUNCTION//ELLIPTIC SOLITONS//ABELIAN FUNCTIONS
10 25091 LPTHIRM//IAESB//WHEATSTONE PHYS

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