Related papers: Constructing Linear Operators Using Classical Pert…
We present a method for the resolution of (oscillatory) nonlinear problems. It is based on the application of the Linear Delta Expansion to the Lindstedt-Poincar\'e method. By applying it to the Duffing equation, we show that our method…
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 apply the Linear Delta Expansion (LDE) to the Lindstedt-Poincare (``distorted time'') method to find improved approximate solutions to nonlinear problems. We find that our method works very well for a wide range of parameters in the case…
The method, proposed in the given work, allows the application of well developed standard methods used in quantum mechanics for approximate solution of the systems of ordinary linear differential equations with periodical coefficients.
We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the…
This work explores the structure of Poincare-Lindstedt perturbation series in Deprit operator formalism and establishes its connection to Kato resolvent expansion. A discussion of invariant definitions for averaging and integrating…
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…
Researchers have developed hybrid Van der Pol Rayleigh Duffing type oscillators to model human induced forces; however, their analytical framework has largely relied on the Lindstedt Poincare perturbation method, energy balance approaches,…
We introduce a framework based on Rockafellar's perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions. Such…
We discuss two alternative methods, based on the Lindstedt--Poincar\'{e} technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches…
This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a complete linear system for the unperturbed problem and,…
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…
By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed…
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt--Poincar\'{e} technique. As illustrative examples we choose one--dimensional anharmonic oscillators…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
We study operator-splitting schemes for approximating Koopman generators of linear semigroups induced by nonlinear flows, a framework originating with Dorroh and Neuberger. Building on ideas of Lie, Kowalewski, and Gr\"{o}bner, we analyze…
We present a method to obtain arbitrarily accurate solutions for conservative classical oscillators. The method that we propose here works both for small and large nonlinearities and provides simple analytical approximations. A comparison…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…