Power solution expansions of the analogue tothe first Painleve equation
Aleksandr D. Bruno, Nikolai A. Kudryashov
Abstract
The fourth-order analog to the first Painlevé equation is studied. All power expansions for solutions of this equation near points z=0 and z=∞ are found. The exponential additions to the expansion of solution near z=∞ are computed. The obtained results confirm the hypothesis that the fourth-order analog of the first Painlevé equation determines new transcendental functions. By means of the methods of power geometry the basis of the plane lattice is also calculated.
Create a lesson
Related papers
Sato-theoretic construction of the anti-self-dual Yang-Mills hierarchy and the Ward conjecture
Shangshuai Li, Da-jun Zhang
Direct linearization, Cauchy matrix and Sato Grassmannian
Kanehisa Takasaki
The transformations of the mToda hierarchy in tau functions
Wenchuang Guan, Shen Wang, Bailin Zhang et al.
Multiparameter Quantum Affine Spaces and the Scalene Yang--Baxter Equation
Pramod Padmanabhan, Somnath Maity, Vladimir Korepin
Long-time asymptotics of the integrable defocusing Wadati-Konno-Ichikawa equation with a finite-genus algebro-geometric background
Taohua Luo, Zhenya Yan, Guoqiang Zhang
New 5th-order Schwarzian evolution equations and their higher-order symmetries
Marianna Euler, Norbert Euler