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Response Solutions for Wave Equations with Variable Wave Speed and Periodic Forcing
We consider a model of nonlinear wave equations with periodically varying wave speed and periodic external forcing. By imposing non-resonance...
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Existence, regularity and symmetry of periodic traveling waves for Gardner–Ostrovsky type equations
We study the existence, regularity and symmetry of periodic traveling solutions to a class of Gardner–Ostrovsky type equations, including the...
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Orbital instability of periodic waves for scalar viscous balance laws
The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral...
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Near-Ordinary Periodic Waves of a Generalized Reaction–Convection–Diffusion Equation
We investigate near-ordinary periodic traveling wave solutions bifurcated from a family of ordinary periodic traveling wave solutions for a...
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Propagation Dynamics of Bistable Traveling Wave to a Time-Periodic Lotka-Volterra Competition Model: Effect of Seasonality
This paper concerns the propagation direction of the bistable traveling wave for a time-periodic Lotka–Volterra reaction–diffusion competition...
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Breather Wave Solutions for the (3+1)-D Generalized Shallow Water Wave Equation with Variable Coefficients
The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a known equation. To achieve...
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Theoretical analysis of surface waves in piezoelectric medium with periodic shunting circuits
The investigations of surface waves in the piezoelectric medium bring out great possibility in designing smart surface acoustic wave (SAW) devices....
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Exact Traveling Wave Doubly Periodic Solutions for Generalized Double Sine-Gordon Equation
The double Sine-Gordon equation is generally used to describe and analyze several physical phenomena in mathematical physics and especially in...
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An adaptive finite element PML method for Helmholtz equations in periodic heterogeneous media
The paper concerns the numerical solution for the wave propagation problem in periodic heterogeneous media. The homogenization method is utilized for...
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Convective Modulation Instability of the Radiation of the Periodic Component in the Case of Resonance of Long and Short Waves
AbstractThe main result of the paper is a theorem stating that the modulation instability of a carrier periodic wave of small (but finite) amplitude...
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Some Abstract Critical Point Theorems and Applications in Wave Equations
With the index defined in [J. Differential Equations, 2016, 260(4): 3749–3784] and [Front. Math., 2023, 18(3): 731–742], we get some critical point...
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Peakon, Periodic Peakons, Compactons and Bifurcations of nonlinear Schrödinger’s Equation with Kudryashov’s Law of Refractive Index
In this paper, we consider the nonlinear Schrödinger’s equation with Kudryashov’s law of refractive index. By using the method of dynamical systems,...
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Local Bifurcation of Steady Almost Periodic Water Waves with Constant Vorticity
In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We...
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Non-separable linear canonical wave packet transform
We introduce the continuous and discrete versions of multi-dimensional linear canonical wave packet transform with the non-separable kernel. At...
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Transverse Dynamics of Two-Dimensional Traveling Periodic Gravity–Capillary Water Waves
We study the transverse dynamics of two-dimensional traveling periodic waves for the gravity–capillary water-wave problem. The governing equations...
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On a Population Model in Discrete Periodic Habitat. II. Bistable Pulsating Waves and Propagation Direction
In this paper, we study bistable pulsating waves for a population model in discrete periodic habitat. After obtaining the existence, uniqueness and...
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Wave Structures in Ideal Gas Flows with an External Energy Source
AbstractWe consider the propagation of plane waves in an ideal gas in the presence of external sources of energy inflow and dissipation. Using the...
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Propagation Dynamics for Time–Space Periodic and Partially Degenerate Reaction–Diffusion Systems with Time Delay
This paper is concerned with the propagation dynamics of a large class of time–space periodic and partially degenerate reaction–diffusion systems...
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Spectral analysis of the periodic b-KP equation under transverse perturbations
The b -family-Kadomtsev–Petviashvili equation ( b -KP) is a two dimensional generalization of the b -family equation. In this paper, we study the...
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Persistence of Kink and Periodic Waves to Singularly Perturbed Two-Component Drinfel’d–Sokolov–Wilson System
This paper concerns the persistence of kink and periodic waves to singularly perturbed two-component Drinfel’d-Sokolov-Wilson system. Geometric...
