Related papers: KAM for the non-linear Beam equation 2: A normal f…

In this paper, we develop an approach to the problem of closing lemma based on KAM normal form. The new approach differs from existing $C^1$ perturbation approach and spectral approach, and can handle the high regularity, high dimensional…

We study perturbations of linear differential equations, deriving explicit series solutions, using Dyson-type expansions. We analyze the monodromy of deformed solutions in a number of examples, and relate this to cocycles in a cohomological…

For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…

In this paper, we revisit the infinite iteration scheme of normal form reductions, introduced by the first and second authors (with Z. Guo), in constructing solutions to nonlinear dispersive PDEs. Our main goal is to present a simplified…

We revisit the dynamics of the post-Newtonian (PN) two-body problem for two inspiraling compact bodies. Starting from a matter-only reduced Hamiltonian, we present an adapted framework based on the Lie series approach, enabling the…

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…

This work is devoted to the strong unique continuation problem for second order parabolic equations with nonsmooth coefficients. Introduction and bibliography have been revised.

Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…

The non-linear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach is based on the 2n + 1 theorem…

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…

In this paper, we investigate a class of doubly nonlinear evolutions PDEs. We establish sharp regularity for the solutions in H\"older spaces. The proof is based on the geometric tangential method and intrinsic scaling technique. Our…

The evolution of the vacuum state in a time-dependent external electric field of arbitrary polarization is investigated within a nonperturbative framework of quantum kinetic equations (QKEs). In our previous work [Phys. Rev. Res. 6, 043009…

We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and…

In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…

In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…

This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…

I propound a non-linear generalization of the Poisson equation describing a "medium" in D dimensions with a "dielectric constant" proportional to the field strength to the power D-2. It is the only conformally invariant scalar theory that…

We present a review of the normal form theory for weakly dispersive nonlinear wave equations where the leading order phenomena can be described by the KdV equation. This is an infinite dimensional extension of the well-known…

We develop a new KAM scheme that applies to SL(2,R) cocycles with one frequency, irrespective of any Diophantine condition on the base dynamics. It gives a generalization of Dinaburg-Sinai's Theorem to arbitrary frequencies: under a…

We extend our previous result on the behavior of the quadratic part of a complex points of a small $\mathcal{C}^{2}$-perturbation of a real $4$-manifold embedded in a complex $3$-manifold. We describe the change of the structure of a normal…