Related papers: Parametric form of QCD travelling waves
Recently, the Whitham and capillary-Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
In this paper we investigate the implementation of the so-called freezing method for second order wave equations in one and several space dimensions. The method converts the given PDE into a partial differential algebraic equation which is…
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…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and traveling wave settings. We adopt a quasi-periodic conformal mapping formulation of the Euler equations,…
Constrained gradient flows are studied in fracture mechanics to describe strongly irreversible (or unidirectional) evolution of cracks. The present paper is devoted to a study on the long-time behavior of non-compact orbits of such…
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, discrete, homogeneous chains with a general power-law contact interaction is studied. For this wave equation,…
We study the existence of monotone traveling wave solutions in a class of nonclassical diffusion equations that include both standard diffusion and a higher-order mixed space-time dispersive term. The reaction term is nonlinear and subject…
Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of them have corresponding traveling waves for the equation…
The variable separated ODE method is extended by choosing the additional variable separated equation as the general elliptic equation. More exact traveling wave solutions of nonlinear equations are obtained by using the method of comparison…
We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate the interest of this model to describe cell motility. The…
We study travelling wave solutions to Korteweg--de Vries type equations which have double power nonlinearities with integer indices, such as the Gardner equation, and fractional dispersion. Whether these equations have ground state…
We consider the coupled electromagnetic waves propagating in a waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. Due to zigzag configuration there are interactions between both nearest…
Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…
We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\frac 12}(\R)$ norm. This fact shows that small data scattering is not…
We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity. Four different types of travelling wave solutions are identified which represent…
In this paper we study the existence of traveling wave solutions for a free-boundary problem modeling the phase transition of a material where the heat is transported by both conduction and radiation. Specifically, we consider a…
In this paper we propose a reduction procedure for determining generalized travelling waves for first order quasilinear hyperbolic nonhomogeneous systems. The basic idea is to look for solutions of the governing model which satisfy a…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…