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...

The effect of weak lateral dispersion of Zakharov-Kutznetsov-type on a Benjamin-Ono solitary wave is studied both asymptotically and numerically. The asymptotic solution is based on an approximate variational solution for the solitary wave, which is then modulated in time through the use of conservation equations. The effect of the dispersive radiation shed as the solitary wave evolves is also ...

We present a KdV-like 2-parameter equation ut + (3(1− δ)u+ (δ + 1)xx ux )ux = εuxxx. By using the dynamical system method, existence of different traveling wave solutions are discussed, including smooth solitary wave solution of with bell type, solitary wave solutions of valley type and peakon wave solution of valley type. Numerical integration are used to shown the different types of solutions...

The existence of a line solitary-wave solution to the water-wave problem with strong surface-tension effects was predicted on the basis of a model equation in the celebrated 1895 paper by D. J. Korteweg and G. de Vries and rigorously confirmed a century later by C. J. Amick and K. Kirchgässner in 1989. A model equation derived by B. B. Kadomtsev and V. I. Petviashvili in 1970 suggests that the ...

in this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order sawada-kotera (ssk) and a lax'sseven-order kdv (lskdv) equations. then obtain the exact solitary-wave so-lutions and numerical solutions of the ssk and lskdv equations for the initialconditions. the numerical solutions are compared with the known analyticalsolutions. their rem...

In the weakly nonlinear long wave régime, internal solitary waves are often modeled by the Korteweg-de Vries equation, which is well-known to support an exact solitary wave solution. However, when the effect of background rotation is taken into account, an additional term is needed and the outcome is the Ostrovsky equation. Although the additional term would appear to be relatively mild, being ...

arises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravitycapillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady water-wave problem. Moreover, all known analytical results for local bifurcations of solitary-wave solutions to the full water-wave problem have precise counterparts fo...

Simulation of free surface flow and sudden wave profile are recognized as the most challenging problem in computational hydraulics. Several Eulerian/Lagrangian approaches and models can be implemented for simulating such phenomena in which the smoothed particle hydrodynamics method (SPH) is categorized as a proper candidate. The incompressible SPH (ISPH) method hires a precise incompressible hy...

Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrödinger equations with attractive self-interaction. However, when selfinteraction becomes repulsive, it seems impossible to have bright solitary wave solution. Here we show that there exists symbiotic bright solitary wave solution of coupled nonlinear Schrödinger equations with repulsive self-interacti...

The long-time asymptotics is analyzed for finite energy solutions of the 1D discrete Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schrödinger equation. T...