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The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…
In the study of evolution equations, the method of adiabatic approximation is an essential tool to reduce an infinite-dimensional dynamical system to a simpler, possibly finite-dimensional one. In this paper, we formulate a generic scheme…
We elaborate a model of the interferometer which, unlike previously studied ones, uses a local (delta-functional) nonlinear repulsive potential, embedded into a harmonic-oscillator trapping potential, as the splitter for the incident…
We compare relativistic approximation methods, which describe gravitational instability in the expanding universe, in a spherically symmetric model. Linear perturbation theory, second-order perturbation theory, relativistic Zel'dovich…
We analyze the transverse instabilities of spatial bright solitons in nonlocal nonlinear media, both analytically and numerically. We demonstrate that the nonlocal nonlinear response leads to a dramatic suppression of the transverse…
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit…
In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…
We consider the radiation transfer problem in the discrete-ordinate, plane-parallel approach. We introduce two benchmark problems with exact known solutions and show that for strongly non-homogeneous media the homogeneous layers…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties. The proposed algorithm is inexact in two sense. First, each proximal subproblem is…
In this paper the theory and simulation results are presented for 3D cylindrical rotationally symmetric spatial soliton propagation in a nonlinear medium using a modified finite-difference time-domain general vector auxiliary differential…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
We compare a particular selection of approximate solutions of the Riemann problem in the context of ideal relativistic magnetohydrodynamics. In particular, we focus on Riemann solvers not requiring a full eigenvector structure. Such solvers…
We introduce a generalized similarity analysis which grants a qualitative description of the localised solutions of any nonlinear differential equation. This procedure provides relations between amplitude, width, and velocity of the…
The intention of this paper is to provide solutions to commutative relations relevant to calculations regarding the hydrogen atom (or similar monoelectronic systems). Though exact solutions exist to these systems, the value to approximation…
We theoretically solve the nonlinear Schr\"{o}dinger equation describing the propagation of pure high, even order dispersion (PHEODs) solitons by variational approach. The Lagrangian for nonlinear pulse transmission systems with each…
We study trapping and propagation of a matter-wave soliton through the interface between uniform medium and a nonlinear optical lattice (NOL). Different regimes for transmission of a broad and a narrow soliton are investigated. Reflections…
We study an intense-short pulse propagation in a saturable cubic-quintic nonlinear media in the presence of nonlinear dispersion within the framework of an extended variational approach. We derive an effective equation for the pulse width…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
The paper deals with the construction of the asymptotic soliton-like and the asymptotic peakon-like solutions to the modified Camassa-Holm equation with variable coefficicents and a singular perturbation. This equation is a generalization…