Related papers: Remarks on the method of comparison equations (gen…
We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds. We do not need to know the explicit formulas for the homoclinic orbits prior…
In this work we study the Ermakov-Lewis invariants of the non-linear Gross-Pitaeviskii equation
Recently, in [arXiv:2403.04827], it was demonstrated that various regular black hole metrics can be derived within a theory featuring an infinite number of higher curvature corrections to General Relativity. Moreover, truncating this…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We give an understanding how strange metals arise from the spatially random Yukawa-SYK model based on the wormhole picture and find a parallelism between the disorder theory and quantum gravity. We start from the observation that the…
We present a general method for the perturbative calculation of the entanglement entropy between two interacting quantum fields. Previous attempts at calculating this quantity perturbatively have encountered a seemingly pathological…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
The Ermakov equation, appearing in quantum mechanics of a harmonic oscillator, is extended via dissipative and thermal terms to take into account the effect of an environment.
A global approximation method of Nystr\"om type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first…
Generalization of the quantum Yang-Baxter equation solutions to an arbitrary grading is studied. The noncommutative differential calculi corresponding to such solutions is considered. The connection with the ordinary and supersymmetric…
In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be "small" in some sense. Indeed, we consider a family of such problems…
We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to…
Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix exponential-like functions on a vector. A very general…
The general solutions with free variable to the second-kind Abel equation, a nonlinear ordinary differential equation that has remained unsolved for nearly two centuries, are presented for the first time by using elementary quadrature…
We begin by introducing the main ideas of the paper under discussion, and we give a brief description of the method proposed. Next, we discuss an alternative approach based on B-spline expansion, and lastly we make some comments on the…
In this article, we study the perturbational method to construct the non-radially symmetric solutions of the compressible 2-component Camassa-Holm equations. In detail, we first combine the substitutional method and the separation method to…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…
The radial component of the motion of compact binary systems composed of neutron stars and/or black holes on eccentric orbit is integrated. We consider all type of perturbations that emerge up to second post-Newtonian order. These…
A differential geometric approach to singular perturbation theory is presented. It is shown that singular perturbation problems such as multiple-scale and boundary layer problems can be treated more easily on a differential geometric basis.…