A model equation for gravity-capillary waves in deep water is proposed. This model is a quadratic approximation of the deep water potential flow equations and has wavepacket-type solitary wave solutions. The model equation supports line solitary waves which are spatially localized in the direction of propagation and constant in the transverse direction, and lump solitary waves which are spatial...

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...

By using the bifurcation theory of dynamical systems to study the dynamical behavior of the Green–Naghdi equations, the existence of solitary wave solutions along with smooth periodic traveling wave solutions is obtained. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact and explicit parametric rep...

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...

Many new solitary wave solutions of the recently studied Lienard equation are obtained by mapping it to the field equation of the φ6−field theory. Further, it is shown that the exact solutions of the Lienard equation are also the exact solutions of the various perturbed soliton equations. Besides, we also consider a one parameter family of generalised Lienard equations and obtain exact solitary...

The goal of this work is to determine whole classes of solitary wave solutions general for wave equations.

The excitation and propagation of finite-amplitude low-frequency solitary waves are investigated in an argon plasma impregnated with kaolin dust particles. A nonlinear longitudinal dust acoustic solitary wave is excited by pulse modulating the discharge voltage with a negative potential. It is found that the velocity of the solitary wave increases and the width decreases with the increase of th...

The joint influence of the polariton effect and Kerr-like nonlinearity on propagation of optical pulses is studied. The existence of different families of envelope solitary wave solutions in the vicinity of polariton gap is shown. The properties of solutions depend strongly on the carrier wave frequency. In particular, solitary waves inside and outside of the polariton gap exhibit different vel...

We consider the nonlinear Schrödinger equation (NLSE) in 1+1 dimension with scalar-scalar self-interaction g(2)/κ+1(ψ*ψ)(κ+1) in the presence of the external forcing terms of the form re(-i(kx+θ))-δψ. We find new exact solutions for this problem and show that the solitary wave momentum is conserved in a moving frame where v(k)=2k. These new exact solutions reduce to the constant phase solutions...

In this paper, new travelling wave solutions to the Fornberg-Whitham equation ut − uxxt + ux + uux = uuxxx + 3uxuxx are investigated. They are characterized by two parameters. The expresssions of the periodic and solitary wave solutions are obtained.