Related papers: Nonlinear Perturbation Theory
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…
We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential…
A novel approach is introduced for deriving exact solutions to nonlinear systems of ordinary differential equations. This method consists of four parts. In the initial part, the examined nonlinear differential equation system is transformed…
It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of…
We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…
The resistance between arbitrary nodes of infinite networks of resistors is studied when the network is perturbed by removing one bond from the perfect lattice. A connection is made between the resistance and the lattice Green's function of…
In this work, we investigate the consistency of a perturbative definition of the S-matrix in a particular class of non-Lagrangian theories. We focus on the $p$-form theories proposed in \cite{Broccoli:2021pvv}, which are fully defined by…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
The solutions to a large class of semi-linear parabolic PDEs are given in terms of expectations of suitable functionals of a tree of branching particles. A sufficient, and in some cases necessary, condition is given for the integrability of…
We analyze random resistor networks through a study of lattice Green's functions in arbitrary dimensions. We develop a systematic disorder perturbation expansion to describe the weak disorder regime of such a system. We use this formulation…
In this paper, we explain a new Iterative Method-Fixed Point and develop its convergence theory for finding approximate solutions of nonlinear equations in the setting of Banach spaces. First, we discuss the convergence analysis of our…
This work is devoted to the study of the existence and sign of Green's functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of $n$-th…
We present a class of solvable models that resemble string theories in many respects but have a strikingly different non-perturbative sector. In particular, there are no exponentially small contributions to perturbation theory in the string…
We address the problem of constructing a non-equilibrium stationary state for a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, using perturbation theory. The linear theory is reviewed, but with the linear…
We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…