Related papers: New exact travelling wave solutions for the K(2,2)…
We prove the existence of highest, cusped, periodic travelling-wave solutions with exact and optimal $ \alpha $-H\"older continuity in a class of fractional negative-order dispersive equations of the form \begin{equation*} u_t + (|…
We investigate the connection between the existence of an explicit travelling wave solution and the travelling wave with minimal speed in a scalar monostable reaction-diffusion equation.
We consider a Fisher-KPP-type equation, where both diffusion and nonlinear part are nonlocal, with anisotropic probability kernels. Under minimal conditions on the coefficients, we prove existence, uniqueness, and uniform space-time…
We present a second kind integral equation (SKIE) formulation for calculating the electromagnetic modes of optical waveguides, where the unknowns are only on material interfaces. The resulting numerical algorithm can handle optical…
We extend the search for traveling-wave asymptotic solutions of the non-linear Balitsky-Kovchegov (BK) saturation equation to non-forward dipole-target amplitudes. Making use of conformal invariant properties of the…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau-Korteweg de Vries equation. We establish existence as well as linear…
We examine travelling wave solutions of the reaction-diffusion equation, $\partial_t u= R(u) + \partial_x \left[D(u) \partial_x u\right]$, with a Stefan-like condition at the edge of the moving front. With only a few assumptions on $R(u)$…
We are concerned with travelling wave solutions arising in a reaction diffusion equation with bistable and nonlocal nonlinearity, for which the comparison principle does not hold. Stability of the equilibrium $u\equiv 1$ is not assumed. We…
This article concerns a class of beam equations with damping on rectangular tori. When the generators satisfy certain relationship, by excluding some value of two model parameters, we prove that such models admit small amplitude…
We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solved for the acoustic particle velocity, mass density, and…
Some systems were recently put forth by Nguyen et. al. as models for studying the interaction of long and short waves in dispersive media. These systems were shown to possess synchronized Jacobi elliptic solutions as well as synchronized…
In this work we study the orbital stability of periodic traveling-wave solutions for dispersive models. The study of traveling waves started in the mid-18th century when John S. Russel established that the flow of water waves in a shallow…
We investigate the existence and spectral stability of traveling wave solutions for a class of fourth-order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization…
We discuss a class of hyperbolic reaction-diffusion equations and apply the modified method of simplest equation in order to obtain an exact solution of an equation of this class (namely the equation that contains polynomial nonlinearity of…
In this manuscript, consideration is given to the existence of periodic traveling-wave solutions to the $abcd$-system. This system was derived by Bona, Saut, and Chen to describe small amplitude, long wavelength gravity waves on the surface…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…
We introduce a new model equation for Stokes gravity waves based on conformal transformations of Euler's equations. The local version of the model equation is relevant for dynamics of shallow water waves. It allows us to characterize the…