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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Defocusing NLS equation with nonzero background: Painleve asymptotics in transition region
非零背景 散焦NLS方程 过渡区 疼痛渐近
2023/5/5
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar steepest descent method and double scaling limit, we obtain Painleve asymptotics in two transitio...
"Quantization" of higher hamiltonian analogues of the Painleve I and Painleve II equations with two degrees of freedom
Quantization higher hamiltonian analogues Painleve I Painleve II equations Exactly Solvable and Integrable Systems
2012/4/27
We construct a solution of an analog of the Schr\"{o}dinger equation for the Hamiltonian $ H_I (z, t, q_1, q_2, p_1, p_2) $ corresponding to the second equation $P_1^2$ in the Painleve I hierarchy. Th...
Painleve Properties and Solution of Revised Camassa-Holm Equation
revised Camassa-Holm equation standard cut-ex pansion non-standard cut-expansion precise solution
2012/9/24
Expansion of Painlevé is one of most effictive methods for solving non-linear partial differential equations. In this paper, using the Painlevé standard and non-standard cut-expansion as well as Maple...
Pade interpolation for elliptic Painleve equation
Pade interpolation elliptic Painleve equation Mathematical Physics
2012/4/17
An interpolation problem related to the elliptic Painlev\'e equation is formulated and solved. A simple form of the elliptic Painlev\'e equation and the Lax pair are obtained. Explicit determinant for...
Point classification of the second order ODE's by Ruslan Sharipov and its application to Painleve equations
Point classification the second order ODE's Ruslan Sharipov Painleve equations
2012/4/17
This is an review on the point classification of second order ODE's by Ruslan Sharipov. His works were published in 1997-1998 at the Electronic Archive at LANL and undeservedly forgotten. Last chapter...
A note on the R. Fuchs's problem for the Painleve equations
Painleve equations Isomonodromic deformation Ordinary differential equations
2012/4/17
In this article we consider a first-order completely integrable system of partial differential equations $\partial \Fi/partial x=A(x, t) \Fi, \partial \Fi/partial t=B(x, t) \Fi$ with $\Fi=(\fi_1, \fi_...
Quantum Painleve-Calogero Correspondence
Quantum Painleve-Calogero Correspondence Mathematical Physics
2011/9/22
Abstract: The Painleve-Calogero correspondence is extended to auxiliary linear problems associated with Painleve equations. The linear problems are represented in a new form which has a suggestive int...
A Class of Special Solutions for the Ultradiscrete Painleve II Equation
ultradiscretization Painleve equation Airy equation q-difference equation
2011/10/9
Abstract: A class of special solutions are constructed in an intuitive way for the ultradiscrete analog of $q$-Painlev\'e II ($q$-PII) equation. The solutions are classified into four groups depending...
Supersymmetric quantum mechanics and Painleve IV equation
Supersymmetric quantum mechanics Painleve IV equation
2011/1/17
It will be seen that the determination of general one-dimensional Schr¨odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev´e IV equation. It shall...
Convergence of iterative methods for Solving Painleve equation
Painlev´ e equation Adomian decomposition method
2010/9/25
In this paper, a Painlev´e equation is solved by using the Adomian’s decomposition method (ADM) , modified Adomian’s decomposition method (MADM), variational iteration method (VIM), modified var...
Integrable Origins of Higher Order Painleve Equations
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
2010/11/10
Higher order Painleve equations invariant under extended affine Weyl groups $A^{(1)}_n$ are obtained through self-similarity limit of a class of pseudo-differential Lax hierarchies with symmetry inher...
The lattice structure of connection preserving deformations for q-Painleve equations I
Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/10
We wish to explore a link between the Lax integrability of the q-Painleve equations and the symmetries of the q-Painleve equations. To do this, we consider the set of associated linear problems for th...
Higher order Painleve system of type D^{(1)}_{2n+2} and monodromy preserving deformation
Painleve system monodromy preserving deformation
2010/11/8
The higher order Painleve system of type D^{(1)}_{2n+2} is proposed by Y. Sasano. It is an extension of the sixth Painleve equation for the affine Weyl group symmetry and expressed as a Hamiltonian sy...
The use of variational iteration method and homotopy perturbation method for Painleve equation I
Painlev`e equations Variational Iteration Method
2010/9/15
In this study, Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM) are employed to approximate solutions of Ppainlev´e equation I, with it’s initial conditions. VIM based o...
We study the underlying relationship between Painleve equations and infinite-dimensional integrable systems, such as the KP and UC hierarchies. We show that a certain reduction of these hierarchies by...