wavelet solutions of the second painleve equation

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Rational Solutions of the Painleve'–vi Equation

In this paper, we classify all values of the parameters α, β, γ and δ of the Painlevé VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlevé VI equation.

Picard and Chazy Solutions to the Painleve’ Vi Equation

Abstract. I study the solutions of a particular family of Painlevé VI equations with the parameters β = γ = 0, δ = 1 2 and 2α = (2μ − 1), for 2μ ∈ Z . I show that the case of half-integer μ is integrable and that the solutions are of two types: the so-called Picard solutions and the so-called Chazy solutions. I give explicit formulae for them and completely determine their asymptotic behaviour ...

wavelet solutions of the klein-gordon equation

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A Brief Survey on the Algebraic Solutions of a Particular Case of the Painleve' Vi Equation

I present here a brief resume, without proofs, of the print \Monodromy of certain Painlev e VI transcendents and reeection groups", written by Prof. Boris Dubrovin and myself (SISSA preprint n. 149=97=FM). In this paper, we study the global analytic properties of the solutions of a particular family of Painlev e VI equations with the parameters = = 0, = 1 2 and arbitrary. We introduce a class o...

STUDYING THE BEHAVIOR OF SOLUTIONS OF A SECOND-ORDER RATIONAL DIFFERENCE EQUATION AND A RATIONAL SYSTEM

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.