相关论文: Flow techniques for non-geometric RDEs on manifold…

We present a new paradigm for Neural ODE algorithms, called ODEtoODE, where time-dependent parameters of the main flow evolve according to a matrix flow on the orthogonal group O(d). This nested system of two flows, where the parameter-flow…

We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar…

We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…

The examples of the Ricci flows on four-dimendionsl manifolds which are determined by help of nonlinear differentials equations of the type of Monge-Ampere are constructed. Their particular solutions and their properties are discussed.

We develop the idea of using an algebraic-geometry approach to classical differential geometry problems. Consider an orthogonal net constructed according to algebraic-geometric data we obtain a set of smooth orthogonal nets that are…

Motivated by the mathematics literature on the algebraic properties of so-called polynomial vector flows, we propose a technique for approximating nonlinear differential equations by linear differential equations. Although the idea of…

Poiseuille flow in cylindrical and planar geometries with a simplified, pseudoplastic (shear thinning) rheology characterized by constant viscosity plateaus above and below a transition strain rate is considered. Analytical, steady state…

We introduce some analytic relations on the set of partial differential equations of two variables. It relies on a new comparison method to give rough asymptotic estimates for solutions which obey different partial differential equations.…

A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…

This paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are…

We construct Riemannian manifolds with completely integrable geodesic flows, in particular various nonhomogeneous examples. The methods employed are a modification of Thimm's method, Riemannian submersions and connected sums.

This article mainly aims to overview the recent efforts on developing algebraic geometry for an arbitrary compact almost complex manifold. We review the results obtained by the guiding philosophy that a statement for smooth maps between…

We study the new geometric flow that was introduced in [11] that evolves a pair of map and (domain) metric in such a way that it changes appropriate initial data into branched minimal immersions. In the present paper we focus on the…

This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This includes Riemannian…

This work concerns the dynamics of nonlinear systems that are subjected to delayed self-feedback. Perturbation methods applied to such systems give rise to slow flows which characteristically contain delayed variables. We consider two…

Recently, J. Streets and G. Tian introduced a natural way to evolve an almost-K\"ahler manifold called the symplectic curvature flow, in which the metric, the symplectic structure and the almost-complex structure are all evolving. We study…

Algebro-geometric solutions for the discrete Chen-Lee-Liu (CLL) system are derived in this paper. We construct a nonlinear integrable symplectic map which is used to define discrete phase flows. Compatibility of the maps with different…

Several results from differential geometry of hypersurfaces in R^n are derived to form a tool box for the direct mapping method. The latter technique has been widely employed to solve problems with moving interfaces, and to study the…

The authors proposed a general way to find particular solutions for overdetermined systems of PDEs previously, where the number of equations is greater than the number of unknown functions. In this paper, we propose an algorithm for finding…

This paper presents a minimum flow approach applicable to a wide range of doubly nonlinear diffusion problems. We introduce a minimum flow steepest descent algorithm that seeks an optimal traffic flow by minimizing an internal energy…