Results 91 to 100 of about 1,141,931 (185)
Painlevé property of the inhomogeneous coupled nonlinear Schrödinger equations
, 1995 We propose a new type of inhomogeneous coupled nonlinear Schrödinger (NLS) equations. Then, we apply the Painlevé singularity structure analysis and find that the proposed equations admit the Painlevé property.
Shanmugha Sundaram, P., Porsezian, K.
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Symmetries in Connection Preserving Deformations
Symmetry, Integrability and Geometry: Methods and Applications, 2011 e wish to show that the root lattice of Bäcklund transformations of the q-analogue of the third and fourth Painlevé equations, which is of type (A_2+A_1)^{(1)}, may be expressed as a quotient of the lattice of connection preserving deformations ...
Christopher M. Ormerod
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Middle Convolution and Heun's Equation
Symmetry, Integrability and Geometry: Methods and Applications, 2009 Heun's equation naturally appears as special cases of Fuchsian system of differential equations of rank two with four singularities by introducing the space of initial conditions of the sixth Painlevé equation.
Kouichi Takemura
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Asymptotics of higher-order Painlevé equations [PDF]
, 2009 We undertake an asymptotic study of a second Painlevé hierarchy based on the Jimbo-Miwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of non-linear ordinary differential equations,
Morrison, Tegan Ann
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Properties of meromorphic solutions of $q$-difference equations
Electronic Journal of Differential Equations, 2015 In this article, we utilize Nevanlinna value distribution theory to study the solvability and the growth of meromorphic function f(z) that satisfies some q-difference equations, which can be seen the q-difference analogues of Painleve I and II ...
Xiaoguang Qi, Lianzhong Yang
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Nonlinear evolution equations and Painlevé test [PDF]
, 1988 This book is an edited version of lectures given by the authors at a seminar at the Rand Afrikaans University. It gives a survey on the Painlevé test, Painlevé property and integrability.
Euler, N, Steeb, Willi-Hans
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Bäcklund transformations for discrete Painlevé equations: Discrete PII-PV
, 2006 Transformation properties of discrete Painlevé equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painlevé equations, discrete PII-PV, with different values of ...
Sakka, Ayman H. +3 more
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Analysis of Singular Solutions of Certain Painlevé Equations [PDF]
, 2018 The six Painlevé equations can be described as the boundary between the non- integrable- and the trivially integrable-systems. Ever since their discovery they have found numerous applications in mathematics and physics.
Twiton, Michael
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FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS
, 2012 We study the underlying relationship between Painlevé equations and infinite-dimensional integrable systems, such as the KP and UC hierarchies. We show that a certain reduction of these hierarchies by requiring homogeneity and periodicity yields ...
TERUHISA TSUDA
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Affine Weyl group approach to Painlevé equations
, 2002 An overview is given on recent developments in the affine Weyl group approach to Painlevé equations and discrete Painlevé equations, based on the joint work with Y.
M. Noumi
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