This paper studies the Klein-Gordon equation with quadratic nonlinearity. The ansatz approach is used to first obtain the singular soliton solution of the equation along with the corresponding domain restriction. The bifurcation analysis is also carried out. By this analysis, a few more traveling wave solutions are retrieved. The bifurcation phase portraits are also given.

This paper describes the design, fabrication, and measurement of backward-wave-cancelled distributed traveling-wave photodetectors. One of the fundamental issues in traveling-wave photodetectors is the generation of backward-waves, which reduces bandwidth or, in the case of matched input termination, reduces their radio-frequency (RF) efficiencies by up to 6 dB. We report a traveling-wave photo...

Khokhlov–Zabolotskaya–Kuznetsov equation (φt + φφx − αφxx)x − 1/2(φyy + φzz) = 0 and its solutions are analyzed. A series of complete exact analytical solutions related to the one-dimensional and vectorial inhomogeneous Burgers equation are presented. A concrete example which corresponds to a special form of the inhomogeneous term is analyzed. Reduction to the traveling wave solution is conside...

Digital waveguide (DW) modeling techniques are typically associated with a traveling-wave decomposition of wave variables and a “reflection function” approach to simulating acoustic systems. As well, it is often assumed that inputs and outputs to/from these systems must be formulated in terms of traveling-wave variables. In this paper, we provide a tutorial review of DW modeling of acoustic str...

Linear reaction-hyperbolic equations arise in the transport of neurofilaments and membrane-bound organelles in axons. The profile of the solution was shown by simulations to be approximately that of a traveling wave; this was also suggested by formal calculations (Reed et al., 1990). In this paper we prove such a result rigorously1.

A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary waves within this family for wide range of parameter values. PACS codes: 02.30.Jr; 47.50.Cd; 83.10.Gr

We consider the Stokes-Boussinesq equations in a slanted (that is, not aligned with gravity’s direction) cylinder of any dimension and with an arbitrary Rayleigh number. We prove the existence of a non-planar traveling wave solution, propagating at a constant speed, and satisfying the Dirichlet boundary condition in the velocity and the Neumann condition in the temperature.

In this paper, we employ the modified simple equation method to find the exact traveling wave solutions involving parameters of nonlinear evolution equations via the (1+1)dimensional generalized shallow water-wave equation and the(2+1)-dimensional KdV-Burgers equation. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave sol...

This article concerns the traveling wave solutions of nonlocal delay reaction-diffusion equations without local quasimonotonicity. The existence of traveling wave solutions is obtained by constructing upper-lower solutions and passing to a limit function. The nonexistence of traveling wave solutions is also established by the theory of asymptotic spreading. The results are applied to a food lim...

Spiral-shaped canyons on the polar ice caps of Mars are striking morphological features whose explanation is still mysterious. We pose a model for the kinetics at the ice-atmosphere interface based on the positive feedback properties of both dust and ice albedo within the north polar ice cap, together with katabatic wind transport of exposed dust. Analysis of this model indicates that traveling...