Related papers: Nonsensitive nonlinear homotopy approach
The relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive…
Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…
Taking advantage of a recent critical point theorem, the existence of infinitely many solutions for an anisotropic problem with a parameter is established. More precisely, a concrete interval of positive parameters, for which the treated…
Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semiclassical models with mode…
Nonlinear topology is an emerging field that combines the intrinsic reconfigurability of nonlinear systems with the robustness of topological protection, offering fertile ground for unconventional phenomena and novel applications. Recently,…
We study the quantum description of parametric heating in harmonic potentials both nonperturbatively and perturbatively, having in mind atom traps. The first approach establishes an explicit connection between classical and quantum…
Dispersionless bands -- flatbands -- have been actively studied thanks to their interesting properties and sensitivity to perturbations, which makes them natural candidates for exotic states. In parallel non-Hermitian systems have attracted…
One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
In this paper we analyze a recently proposed approach for the construction of antisymmetric functions for atomic and molecular systems. It is based on the assumption that the main problems with Hartree-Fock wavefunctions stem from their…
This paper presents a nonlinear approach to measurements a general framework for dealing with variations of environmental conditions. My method may prove promising to extensions beyond classical physics, economics, and other sciences. I…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
We introduce general results on well-posedness and output regulation of regular linear systems with nonautonomous controllers. We present a generalization of the internal model principle for time-dependent controllers with asymptotically…
The importance of ultrasound is well established in the imaging of human tissue. In order to enhance image quality by exploiting nonlinear effects, recently techniques such as harmonic imaging and nonlinearity parameter tomography have been…
The non-Hermitian formalism is used at present in many papers for the description of open quantum systems. A special language developed in this field of physics which makes it difficult for many physicists to follow and to understand the…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a…
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically…
We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial…
Coherent nonlinear optical micro-spectroscopy is a frequently used tool in modern material science, as it is sensitive to many different local observables, which comprise, among others, crystal symmetry and vibrational properties. The…