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A numerical method for analysis and simulation of diffusive viscous wave equations with variable coefficients on polygonal meshes
In this study, we design and analyze weak Galerkin finite element methods to approximate diffusive viscus wave equations with variable coefficients...
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Linear Wave Solutions of a Stochastic Shallow Water Model
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple...
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Mean random attractors of stochastic lattice fractional delay Gray–Scott equations in higher moment product sequence spaces
This paper is devoted to the study of mean attractors in some higher moment product sequence spaces for a three-component reversible lattice...
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Traveling Wave Solutions for Nonlinear Reaction-Diffusion Equations as Dynamical Systems Problems
AbstractIn this paper we present a review of the traveling wave solutions (tws) analysis associated with different families of nonlinear...
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Modulation Instability and Convergence of the Random-Phase Approximation for Stochastic Sea States
The nonlinear Schrödinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of...
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Finite Element Approximations of a Class of Nonlinear Stochastic Wave Equations with Multiplicative Noise
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due...
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Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation
We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic
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Symbolic Computation of Solitary Wave Solutions and Solitons Through Homogenization of Degree
A simplified Hirota method for the computation of solitary waves and solitons of nonlinear partial differential equations (PDEs) is presented. A...
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Exact Traveling Wave Solutions of One-Dimensional Models of Cancer Invasion
AbstractIn this paper, we obtain exact analytical solutions of equations of continuous mathematical models of tumor growth and invasion based on the...
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Recent Progress on the Mathematical Theory of Wave Turbulence
In this note we review some recent progress on the mathematical theory of wave turbulence.
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An Explicit Exponential Integrator Based on Faber Polynomials and its Application to Seismic Wave Modeling
Exponential integrators have been applied successfully in several physics-related differential equations. However, their application in hyperbolic...
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Symplectic dynamical low rank approximation of wave equations with random parameters
In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing...
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Polynomial Mixing of a Stochastic Wave Equation with Dissipative Dam**
We study the long time statistics of a class of semi-linear wave equations modeling the motions of a particle suspended in continuous media while...
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Wave propagation responses of porous bi-directional functionally graded magneto-electro-elastic nanoshells via nonlocal strain gradient theory
This study examines the wave propagation characteristics for a bi-directional functional grading of barium titanate (BaTiO 3 ) and cobalt ferrite (CoFe 2 O...
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Sparse-Stochastic Model Reduction for 2D Euler Equations
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension...
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Optimization of Random Feature Method in the High-Precision Regime
Machine learning has been widely used for solving partial differential equations (PDEs) in recent years, among which the random feature method (RFM)...
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Interpolating the stochastic heat and wave equations with time-independent noise: solvability and exact asymptotics
In this article, we study a class of stochastic partial differential equations with fractional differential operators subject to some...
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Towards Discovery of the Differential Equations
AbstractDifferential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly, in nature-related...
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On Obtaining Initial Approximation for the Full Wave Inversion Problem Using Convolutional Neural Network
AbstractThe paper considers the problem of choosing an initial approximation for gradient optimization methods as applied to the inverse problem of...
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Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations
By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the...