Existence of traveling wave solutions of a high-order nonlinear acoustic wave equation

2009 ◽  
Vol 373 (11) ◽  
pp. 1037-1043 ◽  
Author(s):  
Min Chen ◽  
Monica Torres ◽  
Timothy Walsh
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
High Order ◽  
Acoustic Wave Equation ◽  
Wave Solutions ◽  
Nonlinear Acoustic ◽  
Nonlinear Acoustic Wave

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.

Using a nonlinear acoustic wave equation for anisotropic inversion

2015 ◽  
Author(s):  
Huy Le* ◽  
Biondo Biondi ◽  
Robert G. Clapp ◽  
Stewart A. Levin
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Acoustic Wave Equation ◽  
Nonlinear Acoustic ◽  
Nonlinear Acoustic Wave

Energy-carrying wave simulation of the Lonngren-wave equation in semiconductor materials

2021 ◽  
pp. 2150213
Author(s):  
Hülya Durur
Keyword(s):  
Wave Equation ◽  
Traveling Wave ◽  
Energy Transport ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Discussion Section ◽  
Advantages And Disadvantages ◽  
Wave Solutions ◽  
Package Program

In this study, the Lonngren-wave equation, which is physically semiconductor, is taken into consideration. Traveling wave solutions of this equation are presented with generalized exponential rational function method, which is one of the mathematically powerful analytical methods. These solutions are produced in bright (non-topological) soliton and complex trigonometric-type traveling wave solutions. Three-dimensional (3D), 2D and contour graphics are presented with the help of a ready-made package program with special values given to constants in these solutions. The effect of the change in wave velocity on the traveling wave solution showing energy transport is presented with the help of simulation. It is argued that velocity is one of the important factors in wave diffraction. In the results and discussion section, the advantages and disadvantages of the method are discussed.

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