Submitted: Mar 2, 2013; Accepted: Apr 10, 2013; Published: Jun 10, 2013 Abstract: In this article, we present a variant approach of the generalized and improved (G'/G)–expansion method and construct some new exact traveling wave solutions with free parameters of the nonlinear evolution equations, via the Painleve integrable Burgers equation, the Boiti-Leon-Pempinelle equation and the Pochhammer...

We study the double scaling limit for unitary invariant ensembles of randommatrices with non analytic potentials and find the asymptotic expansion for the entries of the corresponding Jacobi matrix. Our approach is based on the perturbation expansion for the string equations. The first order perturbation terms of the Jacobi matrix coefficients are expressed through the Hastings-McLeod solution ...

Let w(z) be a finite-order meromorphic solution of the second-order difference equation w(z + 1) + w(z − 1) = R(z, w(z)) (†) where R(z, w(z)) is rational in w(z) and meromorphic in z. Then either w(z) satisfies a difference linear or Riccati equation or else equation (†) can be transformed to one of a list of canonical difference equations. This list consists of all known difference Painleve eq...

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these were found. For every type complete list nonequivalent is issued. As exampes equivalence problem for Painleve II equation, III equation with three zero parameters, Emden and some other solved.

Ermakov-Painleve IV coupled systems are introduced and associated Ermakov-type invariants isolated. These used to obtain systematic reduction of the system in terms canonical Painleve equation. The procedure is applied a symmetry derivative resonant nonlinear Schro dinger triad incorporating de Broglie-Bohm potential terms.

We present a study of discrete Painleve equations which do not have any parameter, apart from those that can be removed by the appropriate scaling. find four basic this type as well several more related to ones Miura transformations, we derive explicitly. obtain also continuous limits parameterless and show two them are analogues both I zero-parameter III.