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020 _a9783540398233
_9978-3-540-39823-3
024 7 _a10.1007/BFb0076661
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aIts, Alexander R.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Isomonodromic Deformation Method in the Theory of Painlevé Equations
_h[electronic resource] /
_cby Alexander R. Its, Victor Yu. Novokshenov.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1986.
300 _aCCCXX, 314 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1191
505 0 _aMonodromy data for the systems of linear ordinary differential equations with rational coefficients -- Isomonodromic deformations of systems of linear ordinary differential equations with rational coefficients -- Isomonodromic deformations of systems (1.9) and (1.26) and painlevé equations of II and III types -- Inverse problem of the monodromy theory for the systems (1.9) and (1.26). Asymptotic analysis of integral equations of the inverse problem -- Asymptotic solution to a direct problem of the monodromy theory for the system (1.9) -- Asymptotic solution to a direct problem of the monodromy theory for the system (1.26) -- The manifold of solutions of painlevé II equation decreasing as ? ? ??. Parametrization of their asymptotics through the monodromy data. Ablowitz-segur connection formulae for real-valued solutions decreasing exponentially as ? ? + ? -- The manifold of solutions to painlevé III equation. The connection formulae for the asymptotics of real-valued solutions to the cauchy problem -- The manifold of solutions to painlevé II equation increasing as ? ? + ?. The expression of their asymptotics through the monodromy data. The connection formulae for pure imaginary solutions -- The movable poles of real-valued solutions to painlevé II equation and the eigenfunctions of anharmonic oscillator -- The movable poles of the solutions of painlevé III equation and their connection with mathifu functions -- Large-time asymptotics of the solution of the cauchy problem for MKdV equation -- The dynamics of electromagnetic impulse in a long laser amplifier -- The scaling limit in two-dimensional ising model -- Quasiclassical mode of the three-dimensional wave collapse.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
700 1 _aNovokshenov, Victor Yu.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662214459
776 0 8 _iPrinted edition:
_z9783540164838
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1191
856 4 0 _uhttps://doi.org/10.1007/BFb0076661
912 _aZDB-2-SMA
912 _aZDB-2-LNM
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999 _c12011
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