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A one-dimensional model of a dispersive medium with intrinsic loss, compensated by a parametric drive, is proposed. It is a combination of the well-known parametrically driven nonlinear Schr\"{o}dinger (NLS) and complex cubic…

Pattern Formation and Solitons · Physics 2009-11-10 Hidetsugu Sakaguchi , Boris Malomed

Many supervised machine learning methods have revolutionised the empirical modelling of complex systems. These empirical models, however, are usually "black boxes" and provide only limited physical explanations about the underlying systems.…

Many transitional wall-bounded shear flows are characterised by the coexistence in state-space of laminar and turbulent regimes. Probing the edge boundary between the two attractors has led in the last decade to the numerical discovery of…

Fluid Dynamics · Physics 2017-10-20 Ashley P. Willis , Yohann Duguet , Oleh Omel'chenko , Matthias Wolfrum

We propose and analyze the perfectly matched layer (PML) method for the time-harmonic acoustic waves driven by the white noise source in the presence of the uniform flow. A PML is an artificial absorbing layer commonly used to truncate…

Analysis of PDEs · Mathematics 2015-06-10 Sang-Hyeon Park , Imbo Sim

We develop a structure-preserving computational framework for acoustic wave scattering by moving objects, comprising a new PML-domain-embedding model and a compatible numerical approximation. The model couples a perfectly matched layer…

Numerical Analysis · Mathematics 2026-05-28 Xuelong Gu , Qi Wang

In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite…

Exactly Solvable and Integrable Systems · Physics 2015-03-18 R. Kraenkel , H. Leblond , M. A. Manna

This paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier-Stokes equations in the half line. This is one of the series of papers by the authors on the stability of nonlinear waves…

Analysis of PDEs · Mathematics 2018-11-26 Yazhou Chen , Hakho Hong , Xiaoding Shi

In this paper, a perfectly matched layer (PML) method is proposed to solve the time-domain electromagnetic scattering problems in 3D effectively. The PML problem is defined in a spherical layer and derived by using the Laplace transform and…

Analysis of PDEs · Mathematics 2020-04-24 Changkun Wei , Jiaqing Yang , Bo Zhang

We define a filter of time-frequency anisotropic global singularities of phase space for tempered distributions. The filter contains information from the corresponding anisotropic Gabor wave front set and admits propagation results for the…

Analysis of PDEs · Mathematics 2026-04-22 Luigi Rodino , Patrik Wahlberg

We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation…

Analysis of PDEs · Mathematics 2020-08-14 Paolo Secchi

Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…

Optics · Physics 2011-07-05 Guenbo Hwang , T. R. Akylas , Jianke Yang

We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even…

Fluid Dynamics · Physics 2015-10-08 Suchuan Dong

This is the first of a sequence of four papers \cite{param1}, \cite{param2}, \cite{param3}, \cite{param4} dedicated to the construction and the control of a parametrix to the homogeneous wave equation $\square_{\bf g} \phi=0$, where ${\bf…

Analysis of PDEs · Mathematics 2012-04-10 Jeremie Szeftel

This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a…

Numerical Analysis · Mathematics 2023-06-06 Andrea Mola , Nicola Giuliani , Óscar Crego , Gianluigi Rozza

Unlike an equilibrium gas, the distribution of active particles can be very sensitive to what happens at the boundaries of their container. Experiments and simulations have previously highlighted the possibility of exploiting this behavior…

A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…

Numerical Analysis · Mathematics 2022-07-12 Run Jiang , Yonglin Li , Haijun Wu , Jun Zou

Consider the interaction of biharmonic waves with a periodic array of cavities, characterized by the Kirchhoff--Love model. This paper investigates the perfectly matched layer (PML) formulation and its numerical soution to the governing…

Numerical Analysis · Mathematics 2024-04-23 Peijun Li , Xiaokai Yuan

In this paper, we consider the one-dimensional isentropic compressible Euler equations with linear damping $\beta(t,x)\rho u$ in a bounded domain, which can be used to describe the process of compressible flows through a porous medium.~And…

Analysis of PDEs · Mathematics 2022-07-28 Peng Qu , Huimin Yu , Xiaomin Zhang

A periodically-uneven (in one horizontal direction) stress-free boundary covering a linear, isotropic, homogeneous, lossless solid half space is submitted to a vertically-propagating shear-horizontal plane, body wave. The rigorous theory of…

Computational Physics · Physics 2018-05-28 Armand Wirgin

Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 N. A. Kostov