Solitary wave solutions of the high-order KdV models for bi-directional water waves

2011 ◽  
Vol 16 (3) ◽  
pp. 1314-1328 ◽  
Author(s):  
Georgy I. Burde
Keyword(s):  
Solitary Wave ◽  
Water Waves ◽  
High Order ◽  
Solitary Wave Solutions ◽  
Wave Solutions

scholarly journals Gaussian solitary waves to Boussinesq equation with dual dispersion and logarithmic nonlinearity

2018 ◽  
Vol 23 (6) ◽  
pp. 942-950 ◽  
Author(s):  
Anjan Biswasa ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Trial Function ◽  
Boussinesq Equation ◽  
Solitary Wave Solutions ◽  
Shallow Water Waves ◽  
Wave Solutions ◽  
Extended Trial

This paper discusses shallow water waves that is modeled with Boussinesq equation that comes with dual dispersion and logarithmic nonlinearity. The extended trial function scheme retrieves exact Gaussian solitary wave solutions to the model.

A Generalized Sub-Equation Expansion Method and Some Analytical Solutions to the Inhomogeneous Higher-Order Nonlinear Schrödinger Equation

2008 ◽  
Vol 63 (12) ◽  
pp. 763-777 ◽  
Author(s):  
Biao Li ◽  
Yong Chen ◽  
Yu-Qi Li
Keyword(s):  
Solitary Wave ◽  
Analytical Solutions ◽  
Elliptic Function ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
High Order ◽  
Solitary Wave Solutions ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

On the basis of symbolic computation a generalized sub-equation expansion method is presented for constructing some exact analytical solutions of nonlinear partial differential equations. To illustrate the validity of the method, we investigate the exact analytical solutions of the inhomogeneous high-order nonlinear Schrödinger equation (IHNLSE) including not only the group velocity dispersion, self-phase-modulation, but also various high-order effects, such as the third-order dispersion, self-steepening and self-frequency shift. As a result, a broad class of exact analytical solutions of the IHNLSE are obtained. From our results, many previous solutions of some nonlinear Schrödinger-type equations can be recovered by means of suitable selections of the arbitrary functions and arbitrary constants. With the aid of computer simulation, the abundant structure of bright and dark solitary wave solutions, combined-type solitary wave solutions, dispersion-managed solitary wave solutions, Jacobi elliptic function solutions and Weierstrass elliptic function solutions are shown by some figures.

Exact and explicit solitary wave solutions to a model equation for water waves

1989 ◽  
Vol 139 (8) ◽  
pp. 373-374 ◽  
Author(s):  
Guo-xiang Huang ◽  
Sen-yue Luo ◽  
Xian-xi Dai
Keyword(s):  
Solitary Wave ◽  
Water Waves ◽  
Model Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

scholarly journals Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Weiguo Rui
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Exact Solutions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
High Order ◽  
Solitary Wave Solutions ◽  
Wave Solutions

By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

Sign in / Sign up

Export Citation Format

Share Document