Variational Method to Solitary Wave Solution of the Higher-order Water Wave Equation

2010 ◽  
Vol 11 (Supplement) ◽  
Author(s):  
Yue Wu
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Variational Method ◽  
Wave Solution ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Higher Order

New Solitary Wave Solution for the Boussinesq Wave Equation Using the Semi-Inverse Method and the Exp-Function Method

2009 ◽  
Vol 64 (11) ◽  
pp. 709-712 ◽  
Author(s):  
Wenjun Liu
Keyword(s):  
Wave Equation ◽  
Variational Principle ◽  
Solitary Wave ◽  
Wave Solution ◽  
Variational Formulation ◽  
Function Method ◽  
Inverse Method ◽  
Solitary Wave Solution ◽  
Solitary Solutions

Using the semi-inverse method, a variational formulation is established for the Boussinesq wave equation. Based on the obtained variational principle, solitary solutions in the sech-function and expfunction forms are obtained

scholarly journals Exact dipole solitary wave solution in metamaterials with higher-order dispersion

2016 ◽  
Vol 63 (sup3) ◽  
pp. S44-S50 ◽  
Author(s):  
Xuemin Min ◽  
Rongcao Yang ◽  
Jinping Tian ◽  
Wenrui Xue ◽  
J. M. Christian
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Higher Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

Solitary wave solution to a class of higher-order viscous traffic flow model

2017 ◽  
Vol 31 (13) ◽  
pp. 1750099 ◽  
Author(s):  
Chun-Xiu Wu ◽  
Peng Zhang
Keyword(s):  
Solitary Wave ◽  
Traffic Flow ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Higher Order ◽  
Order Accuracy ◽  
Flow Models ◽  
Weighted Essentially Nonoscillatory ◽  
Traffic Flow Models ◽  
Fifth Order

Traveling waves of a class of higher-order traffic flow models with viscosity are studied with the reduction perturbation method, which leads to the well-known Kortweg–de Vries equation and the approximate solitary wave solution to the model. The fifth-order accuracy weighted essentially nonoscillatory scheme is adopted for comparison between the analytical and numerical results. The numerical tests show that the solitary wave evolves with little deformation of its profile and that a globally perturbed equilibrium traffic state is able to evolve into a profile similar to that of a solitary wave, which is identified by the same total number of vehicles on the ring road. These results are compared with those in the literature and demonstrate that the approximation to the model is more accurate.

THE STABILITY OF THE SOLITARY WAVE SOLUTIONS TO THE GENERALIZED COMPOUND KDV EQUATION

2011 ◽  
Vol 04 (03) ◽  
pp. 475-480
Author(s):  
Xiaohua Liu ◽  
Weiguo Zhang
Keyword(s):  
Solitary Wave ◽  
Variational Method ◽  
Wave Solution ◽  
Lyapunov Functional ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability ◽  
Lyapunov Sense

Using variational method, we investigate that the solitary wave solution u(x - ct) to the Generalized Compound Kdv Equation with two nonlinear terms is stable in the Lyapunov sense when 0 < p < 2 holds. The result is new. There shows a new method to consider the extremum of Lyapunov functional.

Elastic and Annihilation Solitons of the (3+1)-Dimensional Generalized Shallow WaterWave System

2013 ◽  
Vol 68 (5) ◽  
pp. 350-354 ◽  
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang ◽  
Hong-Yu Wu
Keyword(s):  
Exact Solution ◽  
Solitary Wave ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Wave Solution ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Separation Method ◽  
Variable Separation ◽  
Variable Separation Method

With the help of the symbolic computation system Maple, the mapping approach, and a linear variable separation method, a new exact solution of the (3+1)-dimensional generalized shallow water wave (GSWW) system is derived. Based on the obtained solitary wave solution, some novel soliton excitations are investigated.

New Mapping Solutions and Line Soliton Excitations in a (1+1)-Dimensional Dispersive Long-Water Wave System

2013 ◽  
Vol 432 ◽  
pp. 117-121
Author(s):  
Ying Shi ◽  
Bing Ke Wang ◽  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Wave System ◽  
Variable Separation ◽  
New Family ◽  
Localized Excitations ◽  
Variable Separation Approach ◽  
Line Soliton

With the help of the symbolic computation system Maple and the mapping approach and a linear variable separation approach, a new family of exact solutions of the (1+1)-dimensional dispersive long-water wave system (DLWW) is derived. Based on the derived solitary wave solution, some novel localized excitations are investigated.

scholarly journals Approximate asymptotic integration of a higher order water-wave equation using the inverse scattering transform

1997 ◽  
Vol 4 (1) ◽  
pp. 29-53 ◽  
Author(s):  
A. R. Osborne
Keyword(s):  
Wave Equation ◽  
Inverse Scattering ◽  
Water Wave ◽  
Wave Equations ◽  
Solitary Wave Solution ◽  
Laboratory Data ◽  
Inverse Scattering Transform ◽  
Higher Order ◽  
Linear Dispersion ◽  
Scattering Transform

Abstract. The complete mathematical and physical characterization of nonlinear water wave dynamics has been an important goal since the fundamental partial differential equations were discovered by Euler over 200 years ago. Here I study a subset of the full solutions by considering the irrotational, unidirectional multiscale expansion of these equations in shallow-water. I seek to integrate the first higher-order wave equation, beyond the order of the Korteweg- deVries equation, using the inverse scattering transform. While I am unable to integrate this equation directly, I am instead able to integrate an analogous equation in a closely related hierarchy. This new integrable wave equation is tested for physical validity by comparing its linear dispersion relation and solitary wave solution with those of the full water wave equations and with laboratory data. The comparison is remarkably close and thus supports the physical applicability of the new equation. These results are surprising because the inverse scattering transform, long thought to be useful for solving only very special, low-order nonlinear wave equations, can now be thought of as a useful tool for approximately integrating a wide variety of physical systems to higher order. I give a simple scenario for adapting these results to the nonlinear Fourier analysis of experimentally measured wave trains.

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