相关论文: Beyond Linear Decomposition: a Nonlinear Eigenspac…

In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…

We analyse perturbations of self-interacting, scalar field dark matter that contains modes both in a coherent condensate state and an incoherent particle-like state. Starting from the coupled equations for the condensate, the particles'…

For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…

The method due to Nijhoff and Bobenko & Suris to derive Lax pairs for partial difference equations (PDeltaEs) is applied to edge constrained Boussinesq systems. These systems are defined on a quadrilateral. They are consistent around the…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. We study the effect…

Higher-order topological insulators are unusual materials that can support topologically protected states, whose dimensionality is lower than the dimensionality of the structure at least by 2. Among the most intriguing examples of such…

Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…

The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of…

In this article, we aim to study the stability and dynamic transition of an electrically conducting fluid in the presence of an external uniform horizontal magnetic field and rotation based on a Boussinesq approximation model. By analyzing…

Decomposing oceanic and atmospheric flow fields into their slowly evolving balanced components and fast evolving wave components is essential for understanding processes like spontaneous wave emission. To study these processes, the…

Consideration is given to three different full dispersion Boussinesq systems arising as asymptotic models in the bi-directional propagation of weakly nonlinear surface waves in shallow water. We prove that, under a non-cavitation condition…

The Richards equation, a nonlinear elliptic parabolic equation, is widely used to model infiltration in porous media. We develop a finite element method for solving the Richards equation by introducing a new bounded auxiliary variable to…

In this paper we address a particular fluid-solid interaction problem in which the solid object is lying at the bottom of a layer of fluid and moves under the forces created by waves travelling on the surface of this layer. More precisely,…

This paper presents a joint theoretical and numerical study of a stochastic version of the compressible Navier-Stokes equations within the location uncertainty (LU) framework, applied to problems related to upper ocean vertical mixing. This…

Physical systems can be used as an information processing substrate and with that extend traditional computing architectures. For such an application the experimental platform must guarantee pristine control of the initial state, the…

This paper studies the diffusion approximation, non-equilibrium model of radiation hydrodynamics derived by Buet and Despr\'es (J. Quant. Spectrosc. Radiat. Transf. 85 (2004), no. 3-4, 385-418). The latter describes a non-relativistic…

Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…

We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…