WKB analysis of higher order Painlevé equations with a large parameter. II. — Structure theorem for instanton-type solutions of (P J) m (J = I, 34, II-2 or IV) near a simple P-turning point of the first kind

We present a simple derivation of the WKB quantisation condition using the quantum Hamilton-Jacobi formalism and propose an exact quantisation condition within this formalism for integrable models in higher dimensions.

We study the non-perturbative quantum geometry of open and closed topological string on resolved conifold its mirror. Our tools are finite difference equations in moduli resurgence analysis their formal power series solutions. In setting, we derive new for refined partition function as well Nekrasov-Shatashvili (NS) limit. write down a distinguished analytic solution equation that reproduces ex...

We consider the Cauchy-problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of high-frequency asymptotics of such models is reviewed, in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods, leading to ”multi-valued” solutions of Hamilton-Jacobi equations. Using Wigner measures we present an...

We consider a semi-classically scaled Schrödinger equation with WKB initial data. We prove that in the classical limit the corresponding Bohmian trajectories converge (locally in measure) to the classical trajectories before the appearance of the first caustic. In a second step we show that after caustic onset this convergence in general no longer holds. In addition, we provide numerical simula...

We consider the semiclassical Schrödinger-Poisson system with a special initial data of WKB type such that the solution of the limiting hydrodynamical equation becomes time-global in dimensions at least three. We give an example of such initial data in the focusing case via the analysis of the compressible Euler-Poisson equations. This example is a large data with radial symmetry, and is beyond...