Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solut...

Abstract The fractional wave equation is presented as a generalization of the wave equation when arbitrary fractional order derivatives are involved. We have considered variable dielectric environments for the wave propagation phenomena. The Jumarie’s modified Riemann-Liouville derivative has been introduced and the solutions of the fractional Riccati differential equation have been applied to ...

In this paper, using shearlet frames, we present a numerical  method  for solving  the wave equation. We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.

A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional const...

The equal width wave (EW) equation is a model partial differential equation for the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes. The EW-Burgers equation models the propagation of nonlinear and dispersive waves with certain dissipative effects. In this work, we derive exact solitary wave solutions for the general form of the EW equation and the gen...

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 prove some decay estimates of the energy of the wave equation governed by localized nonlinear dissipations in a bounded domain in which trapped rays may occur. The approach is based on a comparison with the linear damped wave equation and an interpolation argument. Our result extends to the nonlinear damped wave equation the well-known optimal logarithmic decay rate for the linear damped wav...

The momentum equation in the kinematic wave model is a power-law equation with two parameters. These parameters, which relate the discharge to the flow area, are commonly derived using Manning’s equation. In general, the values of these parameters depend on the flow depth except for some special cross sections. In this paper, improved estimates of the kinematic wave parameters for circular chan...