Discussions on diffraction and the dispersion for traveling wave solutions of the (2+1)-dimensional paraxial wave equation

2021 ◽  
Author(s):  
Hülya Durur ◽  
Asıf Yokuş
Keyword(s):  
Wave Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Paraxial Wave Equation

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.

scholarly journals Travelling wave solutions for a surface wave equation in fluid mechanics

2016 ◽  
Vol 20 (3) ◽  
pp. 893-898 ◽  
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Wave Equation ◽  
Fluid Mechanics ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Linear Wave ◽  
Travelling Wave Solutions ◽  
Linear Wave Equation ◽  
Wave Solutions

This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

Detection of new multi-wave solutions in an unbounded domain

2019 ◽  
Vol 33 (34) ◽  
pp. 1950425 ◽  
Author(s):  
Mohamed R. Ali ◽  
Wen-Xiu Ma
Keyword(s):  
Wave Equation ◽  
Evolution Equation ◽  
Unbounded Domain ◽  
Traveling Wave ◽  
Water Wave ◽  
Traveling Wave Solutions ◽  
Reduction Process ◽  
Three Dimensions ◽  
Integrating Factor ◽  
Wave Solutions

We deduce new explicit traveling wave solutions for Zoomeron evolution equation and (3[Formula: see text]+[Formula: see text]1)-dimensional shallow water wave equation. The reduction process using Lie vectors leads in some cases to ordinary differential equations (ODEs) that having no quadrature. The integrating factor property has been used to derive several new solutions for these nonsolvable ODEs. These solutions have been illustrated with three dimensions plots. Comparison with other works are presented.

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.

Dynamic interaction of behaviors of time-fractional shallow water wave equation system

2021 ◽  
pp. 2150353
Author(s):  
Serbay Duran
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Traveling Wave Solutions ◽  
Equation System ◽  
Wave Transformation ◽  
Trigonometric Functions ◽  
Shallow Water Wave ◽  
Wave Solutions

In this study, the traveling wave solutions for the time-fractional shallow water wave equation system, whose physical application is defined as the dynamics of water bodies in the ocean or seas, are investigated by [Formula: see text]-expansion method. The nonlinear fractional partial differential equation is transformed to the non-fractional ordinary differential equation with the use of a special wave transformation. In this special wave transformation, we consider the conformable fractional derivative operator to which the chain rule is applied. We obtain complex hyperbolic and complex trigonometric functions for the time-fractional shallow water wave equation system with the help of this technique. New traveling wave solutions are obtained for the special values given to the parameters in these complex hyperbolic and complex trigonometric functions, and the behavior of these solutions is examined with the help of 3D and 2D graphics.

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