Related papers: Quasi-periodic solutions for perturbed generalized…

This paper is concerned with the derivative nonlinear Schrodinger equation with periodic boundary conditions $$\mathbf{i}u_t+u_{xx}+\mathbf{i}\Big(f(x,u,\bar{u})\Big)_x=0,\quad x\in\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z},$$ where $f$ is an…

The question of the total measure of invariant tori in analytic, nearly--integrable Hamiltonian systems is considered. In 1985, Arnol'd, Kozlov and Neishtadt, in the Encyclopaedia of Mathematical Sciences \cite{AKN1}, and in subsequent…

Closed simple integral representation through Vogel's universal parameters is found both for perturbative and nonperturbative (which is inverse invariant group volume) parts of free energy of Chern-Simons theory on $S^3$. This proves the…

Nonperturbative corrections in type II string theory corresponding to Riemann surfaces with one boundary are calculated in several noncompact geometries of desingularized orbifolds. One of these models has a complicated phase structure…

We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…

Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess…

At the light of recent results in literature we review a conjecture formulated in Math. Phys. Electron. J. 1 (1995), paper 5, 1--13, about the mechanism of breakdown of invariant sets in KAM problems and the identification of the dominant…

We prove the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. This result is…

We examine a degenerate, dispersive, nonlinear wave equation related to the evolution of partially molten rock in dimensions two and higher. This simplified model, for a scalar field capturing the melt fraction by volume, has been studied…

We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include the one-dimensional time-independent complex Schr\"odinger equation. Notably,…

A field-theoretical model for non-singular global cosmic strings is presented. The model is a non-linear sigma model with a potential term for a self-gravitating complex scalar field. Non-singular stationary solutions with angular momentum…

We consider the persistence of smooth families of invariant tori in the reversible context 2 of KAM theory under various weak nondegeneracy conditions via Herman's method. The reversible KAM context 2 refers to the situation where the…

In this paper, we study the Hamiltonian systems $ H\left( {y,x,\xi ,\varepsilon } \right) = \left\langle {\omega \left( \xi \right),y} \right\rangle + \varepsilon P\left( {y,x,\xi ,\varepsilon } \right) $, where $ \omega $ and $ P $ are…

Given small initial solutions of the nonlinear quantum harmonic oscillator on $\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as…

A generalisation of the non--perturbatively stable solutions of string equations which respect the KdV flows, obtained recently for the $(2m-1,2)$ conformal minimal models coupled to two--dimensional quantum gravity, is presented for the…

We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non--linear planar double pendulum perturbed by smooth or non--smooth functions.

String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string…

A $U(2)_{L}\times U(2)_{R}$ chiral theory of pseudoscalar, vector, and axial-vector mesons has been proposed. VMD has been revealed from this theory. The physical processes of normal parity and abnormal parity have been studied by using the…

Motivated by quantum gravity on spacetimes with multi-scale geometry, we analyze quantum field theories with a self-adjoint fractional power $(\Box^2)^{\gamma/2}$ of the d'Alem\-bert\-ian in the kinetic term, for any real $\gamma>0$.…

A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…