In this paper, we consider a class of nonlocal equations where the convolution kernel is given by a Bessel potential symbol of order α for α > 1. Based on the properties of the convolution operator, we apply a global bifurcation technique to show the existence of a highest, even, 2 π-periodic traveling-wave solution. The regularity of this wave is proved to be exactly Lipschitz.
In this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations. Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched. Lastly, we show that this type of solution is orbitally stable by periodic perturbations of the same wavelength as the underlying wave.
Abstract
In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.
This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.
Waves of maximal height for a class of nonlocal equations with inhomogeneous symbols