Nonlinear differential or difference equations are encountered not only in mathematics but
also in many areas of physics (evolution equations and propagation of a signal in an optical …

In this article, we construct all fourth‐and fifth‐order differential equations in the polynomial
class having the Painlevé property and having the Bureau symbol P2. The fourth‐order …

In this article, we complete the Painlevé classification of fourth‐order differential equations in
the polynomial class that was begun in paper I, where the subcase having Bureau symbol …

The effect of a small dispersion on the self-focusing of solutions of equations of nonlinear
geometric optics in a spatially one-dimensional case has been studied. This effect in the …

We consider the cubic and quartic Hénon-Heiles Hamiltonians with additional inverse
square terms, which pass the Painlevé test for only seven sets of coefficients. For all the not …

Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems | Journal of
Mathematical Physics | AIP Publishing Skip to Main Content Umbrella Alt Text Umbrella Alt Text …

A classical method of stationary phase for oscillatory integrals is generalized to oscillatory
Riemann–Hilbert problems of the kind arising in the theory of integrable nonlinear …

We construct a solution of an analogue of the Schrödinger equation for the Hamiltonian H 1
(z, t, q 1, q 2, p 1, p 2) corresponding to the second equation P 1 2 in the Painlevé I …

We prove the meromorphy of solutions for a wide class of ordinary differential equations.
These equations are given by invariant manifolds of non-linear partial differential equations …

We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear
Schrödinger equation. If $| n| $< $2 t $, we have decaying oscillation of order $ O (t^{-1/2}) …