Search Results - numerical evolution of nonlinear eigenvalue and eigenvector problems~

Computational Methods and Applications for Numerical Analysis

“…, structure and topology optimization, fractional equations, eigenvalue problems, inverse problems, etc. Numerical analysis is an increasingly…”
Get full text

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics by Roach, G. F, Stratis, Ioannis G, Yannacopoulos, Athanassios N

“…Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature…”
Get full text

Perturbed soliton solutions for an integral modified KdV equation by Saravanan, M., Herman, Russell L.

“… Indeed we focus our attention on a nonlinear evolution equation derived by M. Saravanan and A. Arnaudon (2018 Phys. Lett. A 382 2638) that takes into account the inhomogeneity we are interested…”
Get full text

A local and hierarchical Koopman spectral analysis of fluid dynamics by Zhang, Wei, Wei, Mingjun

“… The continuous and analytic Koopman eigenfunctions and eigenvalues, derived from operator perturbation theory, are capable of dealing with a nonlinear transition process with mathematical rigorousness…”
Get full text

An eigenvalue problem for self-similar patterns in Hele-Shaw flows by Xiao, Wang, Feng, Lingyu, Yang, Fang, Liu, Kai, Zhao, Meng

“… Using a boundary integral formulation, we pose the question of self-similarity as a generalized nonlinear eigenvalue problem, involving two nonlinear integral operators…”
Get full text

Spatial-Dependent Hamiltonian Formulation of Cross-Mode Modulation by Yang, Haofan, Xiong, Zhongfei, Hu, Hanwen, Chen, Yuntian, Zhang, Xinliang, Xu, Jing

“…) under pump-probe configuration is in general complicated because the evolution of the pump light depends on the local mode decomposition of itself…”
Get full text

Spectra of Acoustic-Gravity Waves in the Atmosphere with a Quasi-Isothermal Upper Layer by Kshevetskii, Sergey P., Kurdyaeva, Yuliya A., Gavrilov, Nikolai M.

“… In this paper, we show that this mathematical problem belongs to the class of wave problems having self-adjoint evolution operators, which ensures the correctness and existence of solutions…”
Get full text

Entropy Stable Finite Difference Schemes for Chew, Goldberger and Low Anisotropic Plasma Flow Equations by Singh, Chetan, Yadav, Anshu, Bhoriya, Deepak, Kumar, Harish, Balsara, Dinshaw S.

“…In this article, we consider the Chew, Goldberger and Low (CGL) plasma flow equations, which is a set of nonlinear, non-conservative hyperbolic PDEs modeling anisotropic plasma flows…”
Get full text

Joint Action and Competition between Centrifugal, Magnetorotational, and Magnetic Buoyancy Instabilities by Gradzki, M. J., Hughes, D. W., Mizerski, K. A.

“… The stability problem can be reduced to a second-order boundary value problem…”
Get full text

The Anisotropic Two-Point Correlation Functions of the Nonlinear Traceless Tidal Field in the Principal-Axis Frame by Lee, Jounghun, Hahn, Oliver, Porciani, Cristiano

“…-axis frame, which are measured using numerical data from an N-body simulation. We show that both the nonlinear density and traceless tidal fields are more strongly…”
Get full text

On the structure of solutions of a class of hyperbolic systems with several spatial variables in the far field by Nesterov, A. V.

“…An asymptotic expansion of the solution to the Cauchy problem for a class of hyperbolic weakly nonlinear systems with many spatial variables is constructed…”
Get full text

Two-dimensional ideal magnetohydrodynamic waves on a rotating sphere under a non-Malkus field: I. Continuous spectrum and its ray-theoretical interpretation by Nakashima, Ryosuke, Yoshida, Shigeo

“…Two-dimensional ideal incompressible magnetohydrodynamic (MHD) linear waves at the surface of a rotating sphere are studied as a model to imitate the outermost…”
Get full text

Mathematical analysis of an integral equation arising from population dynamics by Kay, D.A., Sagheer, M., Tang, Q.

“… This equation is first converted to a non-linear integral equation. The discretization and manipulation of the corresponding eigenvalue problem allows us to use the theory…”
Get full text

A dynamic \(p\)-Laplacian by Alvaro de Diego Unanue, Froyland, Gary, Junge, Oliver, Koltai, Péter

“… \(2\)-Laplacian to the standard \(p\)-Laplacian for \(p>1\). Spectral properties of the dynamic Laplacian are connected to the geometric problem of finding…”
Get full text

A Class of Numerical Algorithms for Large Time Integration: The Nonlinear Galerkin Methods by Devulder, Christophe, Marion, Martine

“…The nonlinear Galerkin methods are numerical schemes well adapted to the long-term integration of evolution partial differential equations…”
Get full text

Physics-informed spectral approximation of Koopman operators by Valva, Claire, Giannakis, Dimitrios

“…Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively…”
Get full text

Linear and nonlinear equations for beams and degenerate plates with multiple intermediate piers by Garrione, Maurizio, Gazzola, Filippo

“… The obtained eigenfunctions are used to tackle the study of the nonlinear evolution problem in presence of different nonlinearities, focusing on the appearance of linear…”
Get full text

Sparsity-promoting algorithms for the discovery of informative Koopman invariant subspaces by Pan, Shaowu, Arnold-Medabalimi, Nicholas, Duraisamy, Karthik

“… Well-known techniques such as the dynamic mode decomposition (DMD) and its linear variants provide approximations to the Koopman operator, and have been applied extensively in many fluid dynamic problems…”
Get full text

Koopman Representations in Control by Banks, Michael James

“… These functions are called observables, and their evolution is always linear, even if the underlying dynamical system is nonlinear…”
Get full text

Stability of synchronized dynamics and pattern formation in coupled systems: Review of some recent results by Chen, Yonghong, Rangarajan, Govindan, Ding, Mingzhou

“… These two problems are often treated separately in the literature. Here, we present a unified framework in which we show that the eigenvalues of the coupling matrix…”
Get full text