Related papers: Discussion on exp-function method and modified met…
This survey provides a concise yet comprehensive overview on enhanced dissipation phenomena, transitioning seamlessly from the physical principles underlying the interplay between advection and diffusion to their rigorous mathematical…
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…
We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.
Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations. These extended models are valid one order beyond the usual weakly nonlinear, long wave approximation,…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…
Transformation method provides an efficient way to control wave propagation by materials. However, the degree to which this transformation concept can be applied to other physical phenomena remains an open question. Recently, Hu et al.…
We demonstrate that, if a truncated expansion of a wave function is small, then the standard excited states computational method, of optimizing one root of a secular equation, may lead to an incorrect wave function - despite the correct…
We use the Bethe Ansatz to derive analytical expressions for the current statistics in the asymmetric exclusion process with both forward and backward jumps. The Bethe equations are highly coupled and this fact has impeded their use to…
In this paper we develop a new approximation method valid for a wide family of nonlinear wave equations of Nonlinear Schr\"odinger type. The result is a reduced set of ordinary differential equations for a finite set of parameters measuring…
A coupled boundary spectral element method (BSEM) and spectral element method (SEM) formulation for the propagation of small-amplitude water waves over variable bathymetries is presented in this work. The wave model is based on the…
We propose a new regularization method for constructing a shock wave type solution with nonsmooth front (interaction of shock waves) for quasilinear equations in the one-dimensional case.
This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I with a focus on isomorphs in the low-temperature gas and liquid phases. As expected from the EXP system's strong virial…
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…
Properties of modified plasma waves in non-linear electrodynamics are investigated. We consider a cold, uniform, collisionless, and magnetized plasma model. Initially, we also assume small amplitude waves and the non-relativistic…
We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses St\"urmer's extrapolation formula and assumes…
Based on the Fourier extension, we propose an oversampling collocation method for solving the elliptic partial differential equations with variable coefficients over arbitrary irregular domains. This method only uses the function values on…
We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…