Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines

2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Auxiliary Equation ◽  
Discussion Section ◽  
Auxiliary Equation Method ◽  
Advantages And Disadvantages

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.

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 A New Three Dimensional Dissipative Boussinesq Equation for Rossby Waves and Its Multiple Soliton Solutions☆

2021 ◽  
Author(s):  
Liguo Chen ◽  
Liangui Yang
Keyword(s):  
Rossby Waves ◽  
Boussinesq Equation ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Auxiliary Equation ◽  
Linear Wave ◽  
Auxiliary Equation Method ◽  
Multiple Soliton Solutions ◽  
New Equation

Abstract A new three dimensional nonlinear dynamic theoretical model is derived from fluid mechanics system. In this paper, From the quasi-geostrophic barotropic potential vorticity equation, we obtain a three dimensional dissipative Boussinesq equation by the reduced perturbation method, i.e.utt +e1uxx +e2(u2)xx + e3utxy + e4uxxxx + e5uxxyy = 0. It is emphasized that the new equation is different from the existing Boussinesq equations, which describe the three dimensional nonlinear Rossby waves in the atmosphere. Moreover, we explore the dispersion relation of the linear wave through the new equation. Using the trial function and auxiliary equation method, the two kinds of soliton solutions of the equation are obtained successfully. Finally, the formation mechanism of Rossby waves is discussed by multiple soliton solutions.

scholarly journals BRIGHT AND DARK SOLITON SOLUTIONS OF THE (2 + 1)-DIMENSIONAL EVOLUTION EQUATIONS

2014 ◽  
Vol 19 (1) ◽  
pp. 118-126 ◽  
Author(s):  
Ahmet Bekir ◽  
Adem C. Cevikel ◽  
Ozkan Guner ◽  
Sait San
Keyword(s):  
Solitary Wave ◽  
Nonlinear Equations ◽  
Evolution Equations ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Bright Soliton ◽  
Physical Parameters ◽  
Kp Equation ◽  
Constant Coefficients

In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions and another wave ansatz in the form of tanhp function we obtain exact dark soliton solutions for these equations. The physical parameters in the soliton solutions are obtained nonlinear equations with constant coefficients.

scholarly journals Exact Solutions for a Generalized KdV-MKdV Equation with Variable Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Bo Tang ◽  
Xuemin Wang ◽  
Yingzhe Fan ◽  
Junfeng Qu
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
Auxiliary Equation ◽  
Jacobi Elliptic Function ◽  
Mathematical Tool ◽  
Auxiliary Equation Method

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of variable-coefficient KdV-MKdV equation. As a result, more new exact nontravelling solutions, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, and combined Jacobi elliptic function solutions, for the KdV-MKdV equation are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving many other nonlinear partial differential equations with variable coefficients in mathematical physics.

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