Related papers: Pairwise wave interactions in ideal polytropic gas…
A numerical study of the nonlinear wave solutions of the Rosenau-Pikovsky K(cos) equation is presented. This equation supports at least two kind of solitary waves with compact support: compactons of varying amplitude and speed, both…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
We establish a new geometric wave function that combined with a variational principle efficiently describes a system of bosons interacting in a one-dimensional trap. By means of a a combination of the exact wave function solution for…
A modified version of the conditional symmetry method, together with the classical method, is used to obtain new classes of elliptic solutions of the isentropic ideal compressible fluid flow in (3+1) dimensions. We focus on those types of…
We show that the 1D planar ultrarelativistic shock-tube problem with an ultrarelativistic polytropic equation of state can be solved analytically for the case of a working surface, i.e. for the case when an initial discontinuity on the…
Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…
In this article, we investigate the two-dimensional pressureless Euler equations with three constant Riemann initial data. Our primary focus is on the wave interactions involving contact discontinuities and delta shocks. A distinguishing…
We present the discovery of a class of exact spatially localized as well as periodic wave solutions within the framework of the modified Korteweg-de Vries equation. This class comprises breather and interacting soliton solutions as well as…
In this paper, the equations governing the unsteady flow of a perfect polytropic gas in three space dimensions are considered. The basic similarity reductions for this system are performed. Reduced equations and exact solutions associated…
We present a complete analysis of the dispersion relations for longitudinal and transverse waves in a rarefied polyatomic gas based on Rational Extended Thermodynamics (RET), which describes the evolution of a non-polytropic gas in…
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this…
We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial…
The interaction of elementary waves for isentropic flow in a variable cross-section duct is obtained (\cite{ShengZhang}). The authors have discussed rarefaction wave or shock wave interacts with stationary wave. In this paper, we extend…
In two-dimensional random waves, phase singularities are point-like dislocations with a behavior reminiscent of interacting particles. This -- qualitative -- consideration, stems from the spatial arrangement of these entities, which finds…
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…
This article presents a numerical investigation of overtaking collisions between two solitary waves in the context of the Schamel equation. Our study reveals different regimes characterized by the behavior of the wave interactions. In…
Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between…
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength…