Dynamics of Bright Solitary-waves in a General Fifth-order Shallow Water-wave Model
نویسنده
چکیده
New analytic sech2-type traveling solitary-wave solutions, satisfying zero background at infinity, of a general fifth-order shallow water-wave model are found and compared with previously obtained non-zero background solutions. The allowed coefficient regions for the solitary-wave solutions are classified by requiring the wave number and angular frequency to be real. Detailed numerical simulations are performed to demonstrate the stability of the solitary-waves and to show the soliton-like behavior of two interacting solitary-waves. For a large nonlinear term we show the formation of a bounded state of two solitary-waves, called bion, which travels as a single coherent structure. – PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw
منابع مشابه
High-Order Interaction of Solitary Waves on Shallow Water
The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg–de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations, involving both rightand left-moving wa...
متن کاملInvestigating the Third Order Solitary Wave Generation Accuracy using Incompressible Smoothed Particle Hydrodynamics
This paper examines the generation and propagation of a Third order solitary water wave along the channel. First the Incompressible Smoothed Particle Hydrodynamics (ISPH) numerical method is described and the boundary condition handling method is presented. The numerical model is then used to simulate solitary wave propagation along the fixed depth channel. The numerical results are compared wi...
متن کاملStability of Solitary Waves of a Fifth-Order Water Wave Model
We consider the stability of solitary waves of a class of 5th order KdV equations. It is known that their stability is determined by the second derivative of a function of the wave speed d(c). We perform a detailed investigation of the properties of this function, both analytically and numerically. For a class of homogeneous nonlinearities, we precisely determine the regions of wave speeds for ...
متن کاملInvestigating the Amount of Forces Caused by Solitary Waves on Coastal Walls Using OpenFOAM Software
Coastal walls (dyke) are one of the methods of protecting the coast against coastal erosion and destructive forces of waves. The purpose of this study is to simulate the wave collision with the coastal dyke and compare the results with the laboratory model. Open FOAM open source software and K-ω SST turbulence model were used to simulate the amount of wave consumed by the coastal dyke. Taking i...
متن کاملMultipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms
We consider a high-order nonlinear Schrödinger (HNLS) equation with thirdand fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and ...
متن کامل