scholarly journals New Exact Solutions, Dynamical and Chaotic Behaviors for the Fourth-Order Nonlinear Generalized Boussinesq Water Wave Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Cheng Chen ◽  
Zuolei Wang
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Fourth Order ◽  
Water Wave ◽  
Wave Transformation ◽  
Physical Parameters ◽  
New Exact Solutions ◽  
Dynamical Behaviors ◽  
Cklund Transformation ◽  
Homogeneous Balance Method

Based on the extended homogeneous balance method, the auto-B a ¨ cklund transformation transformation is constructed and some new explicit and exact solutions are given for the fourth-order nonlinear generalized Boussinesq water wave equation. Then, the fourth-order nonlinear generalized Boussinesq water wave equation is transformed into the planer dynamical system under traveling wave transformation. We also investigate the dynamical behaviors and chaotic behaviors of the considered equation. Finally, the numerical simulations show that the change of the physical parameters will affect the dynamic behaviors of the system.

New Exact Solutions for Two Nonlinear Equations

2006 ◽  
Vol 61 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Zonghang Yang
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Exact Solutions ◽  
Water Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
New Exact Solutions ◽  
Complex Phenomena ◽  
Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

scholarly journals New exact solutions of a generalized shallow water wave equation

2010 ◽  
Vol 82 (2) ◽  
pp. 025003 ◽  
Author(s):  
Bijan Bagchi ◽  
Supratim Das ◽  
Asish Ganguly
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Shallow Water Wave ◽  
New Exact Solutions

scholarly journals New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using the Multiple Simplest Equation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Yun-Mei Zhao
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Water Wave ◽  
Type Equation ◽  
Wave Model ◽  
Rational Functions ◽  
Equation Method ◽  
Number Of Solutions ◽  
New Exact Solutions ◽  
Simplest Equation Method

In our work, a generalized KdV type equation of neglecting the highest-order infinitesimal term, which is an important water wave model, is discussed by using the simplest equation method and its variants. The solutions obtained are general solutions which are in the form of hyperbolic, trigonometric, and rational functions. These methods are more effective and simple than other methods and a number of solutions can be obtained at the same time.

Solitary dynamics of longitudinal wave equation arises in magneto-electro-elastic circular rod

2020 ◽  
pp. 2150086 ◽  
Author(s):  
Naila Sajid ◽  
Ghazala Akram
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Mapping Method ◽  
Integration Scheme ◽  
Auxiliary Equation ◽  
New Exact Solutions ◽  
Non Linear ◽  
Physical Phenomena

This paper examines the effectiveness of an integration scheme, which called the extended modified auxiliary equation mapping method in exactly solving a well-known non-linear longitudinal wave equation with dispersion caused by transverse Poisson’s effect arises in a magneto-electro-elastic (MEE) circular rod. Explicit new exact solutions are derived in different form such as hyperbolic, kinky, anti-kinky, dark, and singular solitons of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena.

Exact solutions of a (2+1)-dimensional extended shallow water wave equation

2019 ◽  
Vol 28 (10) ◽  
pp. 100202 ◽  
Author(s):  
Feng Yuan ◽  
Jing-Song He ◽  
Yi Cheng
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Shallow Water Wave
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