scholarly journals Lagrangian Formulation, Conservation Laws, Travelling Wave Solutions: A Generalized Benney-Luke Equation

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1480
Author(s):  
Sivenathi Oscar Mbusi ◽  
Ben Muatjetjeja ◽  
Abdullahi Rashid Adem
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Density ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Noether Symmetries ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method ◽  
Derivatives Of

The aim of this paper is to find the Noether symmetries of a generalized Benney-Luke equation. Thereafter, we construct the associated conserved vectors. In addition, we search for exact solutions for the generalized Benney-Luke equation through the extended tanh method. A brief observation on equations arising from a Lagrangian density function with high order derivatives of the field variables, is also discussed.

scholarly journals On the Solutions and Conservation Laws of a Coupled Kadomtsev-Petviashvili Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Travelling Wave ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Scientific Applications ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Petviashvili Equation

A coupled Kadomtsev-Petviashvili equation, which arises in various problems in many scientific applications, is studied. Exact solutions are obtained using the simplest equation method. The solutions obtained are travelling wave solutions. In addition, we also derive the conservation laws for the coupled Kadomtsev-Petviashvili equation.

scholarly journals Travelling wave solutions for the generalized Schrödinger equation

2021 ◽  
Vol 2090 (1) ◽  
pp. 012062
Author(s):  
G.N. Shaikhova ◽  
B.K. Rakhimzhanov ◽  
Zh.K. Zhanbosinova
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Extended Tanh Method ◽  
Physical Problems ◽  
Wave Solutions ◽  
Tanh Method ◽  
Different Types

Abstract In this work, the generalized nonlinear Schrödinger equation is investigated. This equation is integrable and admits Lax pair. To obtain travelling wave solutions the extended tanh method is applied. This method is effective to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The derived solutions are found to be important for the explanation of some practical physical problems.

Travelling Wave Solutions for Generalized Pochhammer-Chree Equations

2002 ◽  
Vol 57 (11) ◽  
pp. 874-882 ◽  
Author(s):  
Biao Li ◽  
Yong Chen ◽  
Hongqing Zhang
Keyword(s):  
Periodic Solutions ◽  
Symbolic Computation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Rational Solutions ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method ◽  
Wave Reduction

In this paper, by means of a proper transformation and symbolic computation, we study the travelling wave reduction for the generalized Pochhammer-Chree (PC) equations (1.3) and (1.4) by use of the recently proposed extended-tanh method. As a result, rich travelling wave solutions, which include kink-shaped solitons, bell-shaped solitons, periodic solutions, rational solutions, singular solitons, are obtained. At the same time, using a direct assumption method, the more general bell-shaped solitons for the generalized PC Eq. (1.3) are obtained. The properties of the solutions are show in figures.

scholarly journals Travelling Wave Solutions for Two Generalized Hirota-Satsuma Coupled KdV Systems

2001 ◽  
Vol 56 (3-4) ◽  
pp. 312-318 ◽  
Author(s):  
Engui Fan
Keyword(s):  
Full Advantage ◽  
Riccati Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Symbolic Computations ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method

Abstract In this paper we present an extended tanh method that utilizes symbolic computations to obtain more travelling wave solutions for two generalized Hirota-Satsuma coupled KdV systems in a unified way. The key idea of this method is to take full advantage of a Riccati equation involving a parameter and use its solutions to replace the tanh-function by the tanh method. It is quite interesting that the numbers and types of the traveling wave solutions can be judged from the sign of the parameter. In this paper we investigate the two generalized Hirota-Satsuma coupled KdV systems

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

Generalized tanh Method Extended to Special Types of Nonlinear Equations

2002 ◽  
Vol 57 (8) ◽  
pp. 692-700 ◽  
Author(s):  
Engui Fan ◽  
Y. C. Hona
Keyword(s):  
Nonlinear Equations ◽  
Gordon Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Sine Gordon Equation ◽  
Wave Solutions ◽  
Tanh Method

By some ‘pre-possessing’ techniques we extend the generalized tanh method to special types of nonlinear equations for constructing their multiple travelling wave solutions. The efficiency of the method can be demonstrated for a large variety of special equations such as those considered in this paper, double sine-Gordon equation, (2+1)-dimensional sine-Gordon equation, Dodd-Bullough- Mikhailov equation, coupled Schrödinger-KdV equation and (2+1)-dimensional coupled Davey- Stewartson equation. - Pacs: 03.40.Kf; 02.30.Jr.

scholarly journals Travelling Wave solutions of hyperbolic Telegraph equation by Tanh method

2021 ◽  
Vol 12 (2) ◽  
pp. 3032-3035
Author(s):  
Anjali Verma, Et. al.
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Telegraph Equation ◽  
Travelling Wave ◽  
Second Order ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Tanh Method ◽  
Convenient Approach ◽  
Nonlinear Telegraph Equation

Tanh method is utilized to find travelling solutions of second order nonlinear Telegraph equation. As a result, we attain dissimilar travelling wave solutions. Our aim is to show that this method is most efficient and convenient approach for verdict travelling wave solutions of nonlinear differential equations. For calculation the software MAPLE is used.

scholarly journals Exact Solutions for the Wick-Type Stochastic Schamel-Korteweg-de Vries Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Xueqin Wang ◽  
Yadong Shang ◽  
Huahui Di
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Vries Equation ◽  
Expansion Method ◽  
Travelling Wave ◽  
Variable Coefficients ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Hermite Transformation

We consider the Wick-type stochastic Schamel-Korteweg-de Vries equation with variable coefficients in this paper. With the aid of symbolic computation and Hermite transformation, by employing the (G′/G,1/G)-expansion method, we derive the new exact travelling wave solutions, which include hyperbolic and trigonometric solutions for the considered equations.

scholarly journals Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin–Bona–Mahony Equations

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 134 ◽  
Author(s):  
Praveen Agarwal ◽  
Abd-Allah Hyder ◽  
M. Zakarya ◽  
Ghada AlNemer ◽  
Clemente Cesarano ◽  
...  
Keyword(s):  
Exact Solutions ◽  
White Noise ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Hermite Transform ◽  
Wave Solutions ◽  
White Noise Functional

In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling wave solutions for the (3+1)-dimensional modified BBM equations. This set includes solutions of exponential, hyperbolic, and trigonometric types. With the help of inverse Hermite transform, we obtained stochastic travelling wave solutions for the Wick-type stochastic (3+1)-dimensional modified BBM equations. Eventually, by application example, we show how the stochastic solutions can be given as white noise functional solutions.

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