Related papers: Nonlinear trident using WKB and worldline instanto…
We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose…
The three-wave resonant interaction equations are a non-dispersive system of partial differential equations with quadratic coupling describing the time evolution of the complex amplitudes of three resonant wave modes. Collisions of wave…
The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev-Petviashvili (enKP) model through a systematic analysis of…
Nonlinear phenomena of lepton-photon interactions in external backgrounds with a generalised periodic plane-wave geometry are studied. We discuss nonlinear Compton scattering in head-on lepton-photon collisions extended properly to beyond…
We propose two efficient energetic spectral-element methods in time for marching nonlinear gradient systems with the phase-field Allen--Cahn equation as an example: one fully implicit nonlinear method and one semi-implicit linear method.…
We apply the worldline formalism to scalar quantum electrodynamics (QED) to find a Bern-Kosower type master formula for generalized Compton scattering, on-shell and off-shell. Moreover, we use it to study the non-perturbative gauge…
We present theoretical foundations and numerical demonstration of an efficient method for performing time-dependent many-electron simulations for electronic transport. The method employs the concept of stroboscopic wavepacket basis for the…
We study the energy-critical wave equation in three dimensions, focusing on its ground state soliton, denoted by $W$. Using the Poincar\'e symmetry inherent in the equation, boosting $W$ along any timelike geodesic yields another solution.…
We study the equations of Wheeler-Feynman electrodynamics which is an action-at-a-distance theory about world-lines of charges that interact through their corresponding advanced and retarded Li\'enard-Wiechert field terms. The equations are…
The non-perturbative dynamics of quantum field theories is studied using theoretical tools inspired by string formalism. Two main lines are developed: the analysis of stringy instantons in a class of four-dimensional N=2 gauge theories and…
We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations…
The exponential B-spline basis function set is used to develop a collocation method for some initial boundary value problems (IBVPs) to the Gardner equation. The Gardner equation has two nonlinear terms, namely quadratic and cubic ones. The…
The Wheeler-DeWitt equation for the induced gravity theory is constructed in the minisuperspace approximation, and then solved using the WKB method under three types of boundary condition proposed respectively by Hartle & Hawking (``no…
We use the worldline formalism for calculating the one-loop effective action for the Einstein-Maxwell background induced by charged scalars or spinors, in the limit of low energy and weak gravitational field but treating the electromagnetic…
Considering the nonlinear electromagnetic field coupled to Einstein gravity in the presence of cosmological constant, we obtain a new class of $d$-dimensional magnetic brane solutions. This class of solutions yields a spacetime with a…
In this paper we develop a formalism to analyze the spectrum of small perturbations about arbitrary solutions of Einstein, Yang-Mills and scalar systems. We consider a general system of gravitational, gauge and scalar fields in a…
We study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah--Struwe solutions, which satisfy the Strichartz estimates and are coincide with the class of…
This paper introduces "time-dependent basis light-front quantization", which is a covariant, nonperturbative, and first principles numerical approach to time-dependent problems in quantum field theory. We demonstrate this approach by…