Travelling wave solutions and soliton solutions for the nonlinear transmission line using the generalized Riccati equation mapping method

2015 ◽  
Vol 84 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Boudoue Hubert Malwe ◽  
Gambo Betchewe ◽  
Serge Y. Doka ◽  
Timoleon Crepin Kofane
Keyword(s):  
Transmission Line ◽  
Riccati Equation ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Mapping Method ◽  
Travelling Wave Solutions ◽  
Nonlinear Transmission Line ◽  
Nonlinear Transmission ◽  
Wave Solutions ◽  
Generalized Riccati Equation

Exact and soliton solutions to nonlinear transmission line model

2016 ◽  
Vol 87 (2) ◽  
pp. 767-773 ◽  
Author(s):  
M. M. El-Borai ◽  
H. M. El-Owaidy ◽  
H. M. Ahmed ◽  
A. H. Arnous
Keyword(s):  
Transmission Line ◽  
Soliton Solutions ◽  
Transmission Line Model ◽  
Nonlinear Transmission Line ◽  
Line Model ◽  
Nonlinear Transmission

scholarly journals Abundant Exact Solition-Like Solutions to the Generalized Bretherton Equation with Arbitrary Constants

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xiuqing Yu ◽  
Fengsheng Xu ◽  
Lihua Zhang
Keyword(s):  
Full Advantage ◽  
Riccati Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

The Riccati equation is employed to construct exact travelling wave solutions to the generalized Bretherton equation. Taking full advantage of the Riccati equation which has more new solutions, abundant new multiple solition-like solutions are obtained for the generalized Bretherton equation.

Bright soliton solutions, power series solutions and travelling wave solutions of a (3+1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (06) ◽  
pp. 1850082
Author(s):  
Ding Guo ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Bright Soliton ◽  
Travelling Wave Solutions ◽  
Series Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Power Series Solutions ◽  
De Vries

In this paper, we consider the (3[Formula: see text]+[Formula: see text]1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdV-KP) equation, which can be used to describe the nonlinear waves in plasma physics and fluid dynamics. By using solitary wave ansatz in the form of sech[Formula: see text] function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively. Moreover, we obtain its power series solutions with the convergence analysis. It is hoped that our results can provide the richer dynamical behavior of the KdV-type and KP-type equations.

Three Kind of Triangle Rational Functions and Applications for Discrete Nonlinear Equations

2011 ◽  
Vol 317-319 ◽  
pp. 2168-2171
Author(s):  
Xiu Rong Guo ◽  
Zheng Tao Liu ◽  
Mei Guo
Keyword(s):  
Nonlinear Equations ◽  
Difference Equations ◽  
Soliton Solutions ◽  
Rational Functions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Periodic Travelling Wave ◽  
Formal Solutions

In order to efficiently search for new soliton solutions to differential-difference equations (DDEs), three kinds of triangle rational functions are first introduced. Then a kind of formal solutions of DDEs are presented which are expressed by a unified nonlinear combination of the three kinds of triangle rational functions. As illustrative examples, the periodic travelling-wave solutions of the discrete modified KdV(mKdV) equations are obtained.

New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method

2010 ◽  
Vol 65 (3) ◽  
pp. 197-202 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symbolic Computation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary solutions for the Chaffee-Infante equation with distinct physical structures. The results reveal that the exp-function method is suited for finding travelling wave solutions of nonlinear partial differential equations arising in mathematical physics

scholarly journals Method for Studying the Multisoliton Solutions of the Korteweg-de Vries Type Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yuriy Turbal ◽  
Andriy Bomba ◽  
Mariana Turbal
Keyword(s):  
Soliton Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
New Approach ◽  
Wave Solutions ◽  
De Vries ◽  
Multisoliton Solutions

We present a new approach to find travelling wave solutions for the Korteweg-de Vries type equations, which allows extending the class of known soliton solutions. Also we propose method for studying the multisoliton solutions of the Korteweg-de Vries type equations.

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