Cochlear emissions provide a noninvasive probe of cochlear mechanics, but their utility is hindered by incomplete understanding of their relationship to intracochlear activity. In particular, recent work has uncovered a question about the mode by which emissions travel out of the cochlea -whether they emerge via a “fast” compression pressure or a “slow” traveling-wave pressure. We further probe...

Ray-wave geometric beam is an exotic kind of structured light with ray-wave duality and coupled diverse degrees freedom (DoFs), which has attracted intense attention due to its potential applications in theories applications. This work offers a new insight that the traditional beams can be seen as transverse standing-wave (SW) beams, decomposed into superposition traveling-wave (TW) beams. We c...

Traveling wave solutions to a class of dispersive models, ut − utxx + uux = θuuxxx + (1− θ)uxuxx, are investigated in terms of the parameter θ, including two integrable equations, the Camassa-Holm equation, θ = 1/3, and the Degasperis-Procesi equation, θ = 1/4, as special models. It was proved in [H. Liu and Z. Yin, Contemporary Mathematics, 2011, 526, pp273–294] that when 1/2 < θ ≤ 1 smooth so...

In this paper, based on the known first integral method, we try to seek the traveling wave solutions of several nonlinear evolution equations. As a result, some exact travelig wave solutions and solitary solutions for Whitham-Broer-Kaup (WBK) equations, Gardner equation, Boussinesq-Burgers equations, nonlinear schrodinger equation and mKDV equation are established successfully. Key–Words: First...

We show that finite external excitation can lead to a traveling wave in an excitable passive optical system with one-dimensional space geometry. We have studied the excitable behavior of this system in parallel with that of its diffusive counterpart and show the effects of optical phase on the traveling-wave solution and its velocity. In two-dimensional space we observe numerically rotating opt...

We investigate traveling wave solutions to a class of dispersive models – the θ-equation of the form ut − utxx + uux = θuuxxx + (1− θ)uxuxx, including two integrable equations, the Camassa-Holm equation (θ = 1/3) and the Degasperis-Procesi equation(θ = 1/4) as special models. When 0 ≤ θ ≤ 1 2 , strong solutions of the θ-equation may blow-up in finite time, correspondingly, the traveling wave so...

In this paper, we consider the spatial dynamics for a non-cooperative diffusion system arising from epidermal wound healing. We shall establish the spreading speed and existence of traveling waves and characterize the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. We also construct some new types of entire solutions which are different from the travel...

In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c∗, and show the existence of traveling plane wave solutions conn...

We obtain existence of traveling wave solutions for a class of spatially discrete systems, namely lattice di erential equations. Uniqueness of the wave speed c, and uniqueness of the solution with c 6= 0, are also shown. More generally, the global structure of the set of all traveling wave solutions is shown to be a smooth manifold where c 6= 0. Convergence results for solutions are obtained at...

We study the traveling wave front solutions for a two-dimensional periodic lattice dynamical system with monostable nonlinearity. We first show that there is a minimal speed such that a traveling wave solution exists if and only if its speed is above this minimal speed. Then we prove that any wave profile is strictly monotone. Finally, we derive the convergence of discretized minimal speed to t...