Numerical Solution of Some Nonlocal , Nonlineardispersive Wave
نویسندگان
چکیده
We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial prooles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the innnite depth limit, is the one predicted by the theory.
منابع مشابه
Thermal vibration analysis of double-layer graphene embedded in elastic medium based on nonlocal continuum mechanics
This paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. The graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. Nonlocal governing equations of motion for this double-layer graphene s...
متن کاملThermal vibration analysis of double-layer graphene embedded in elastic medium based on nonlocal continuum mechanics
This paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. The graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. Nonlocal governing equations of motion for this double-layer graphene s...
متن کاملExact analytical approach for free longitudinal vibration of nanorods based on nonlocal elasticity theory from wave standpoint
In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus, it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...
متن کاملNumerical solution of an initial-boundary value problem with nonlocal condition for the wave equation
This paper investigates an initial-boundary value problem with nonlocal condition for the wave equation. The numerical solution is developed by using Homotopy perturbation method. This method is based on the use of traditional perturbation method and homotopy technique. Using this method, a rapid convergent series solution can be obtained in most cases. Furthermore, this method does not require...
متن کاملNumerical studies of non-local hyperbolic partial differential equations using collocation methods
The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...
متن کامل