Related papers: Large-order perturbation theory of linear eigenval…

The perturbation theory based on the Riemann-Hilbert problem is developed for the modified nonlinear Schr{\"o}dinger equation which describes the propagation of femtosecond optical pulses in nonlinear single-mode optical fibers. A detailed…

We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function,…

We discuss linearized gravitational perturbations of higher dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric…

An overview is given of the methods for treating complicated problems without small parameters, when the standard perturbation theory based on the existence of small parameters becomes useless. Such complicated problems are typical of…

Singular perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact…

We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed…

We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the…

We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of…

Starting from degree N solutions of a time dependent Schroedinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around the N zeros of the polynomial is derived. The matrix has…

We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become…

Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that…

The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…

We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling…

The perturbation theory plays an important role in studying structure formation in cosmology and post-Newtonian physics, but not all phenomena can be described by the linear perturbation theory. Thus, It is necessary to study exact…

We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…

In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…

In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well…

We consider the Dirichlet Laplacian in a straight three dimensional waveguide with non-rotationally invariant cross section, perturbed by a twisting of small amplitude. It is well known that such a perturbation does not create eigenvalues…

We present a method which allows to deform extremal black hole solutions into non-extremal solutions, for a large class of supersymmetric and non-supersymmetric Einstein-Vector-Scalar type theories. The deformation is shown to be largely…

We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…