Related papers: Perturbation theory for nearly integrable multi-co…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
We develope a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs). In particular, we estimate the $…
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…
This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda…
We introduce a general framework of low regularity integrators which allows us to approximate the time dynamics of a large class of equations, including parabolic and hyperbolic problems, as well as dispersive equations, up to arbitrary…
We present an elementary pedagogical derivation of the Brillouin-Wigner and the Rayleigh-Schr\"odinger perturbation theories with Epstein-Nesbet partitioning. A variant of the Brillouin-Wigner perturbation theory is also introduced, which…
We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our…
We have developed a variational perturbation theory based on the Liouville-Neumann equation, which enables one to systematically compute the perturbative correction terms to the variationally determined wave functions of the time-dependent…
We develop a perturbation theory for bright solitons of the F=1 integrable spinor Bose-Einstein condensate (BEC) model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution…
We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard…
We present a high order perturbation approach to quantitatively calculate spectral densities in three distinct steps starting from the model Hamiltonian and the observables of interest. The approach is based on the perturbative continuous…
An explicit perturbative solution to all orders is given for a general class of nonlinear differential equations. This solution is written as a sum indexed by rooted trees and uses the Green function of a linearization of the equations. The…
The perturbed NLS equation is asymptotically integrable if the zero-order approximation to the solution is a single soliton. It is not integrable for any other zero-order solution. In the standard application of a Normal Form expansion,…
We present a new perturbative formulation of non-equilibrium thermal field theory, based upon non-homogeneous free propagators and time-dependent vertices. The resulting time-dependent diagrammatic perturbation series are free of pinch…
Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…
The Novikov-Veselov (NV) equation is a dispersive (2+1)-dimensional nonlinear evolution equation that generalizes the (1+1)-dimensional Korteweg-deVries (KdV) equation. This paper considers the stability of plane wave soliton solutions of…
Multitime evolution PDEs for Rayleigh waves are considered, using geometrical ingredients capable to build an ultra-parabolic-hyperbolic differential operator. Their soliton solutions are found based on appropriate hypotheses and specific…
The goal of this work is to revisit the eigenfunction-expansion-based perturbation theory for the defocusing nonlinear Schr\"odinger equation a nonzero background, and develop it to correctly predict the slow-time evolution of the dark…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means…