scholarly journals Lie Symmetry Reductions and Exact Solutions to the Rosenau Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ben Gao ◽  
Hongxia Tian
Keyword(s):  
Exact Solutions ◽  
Analytic Solutions ◽  
Lie Symmetry ◽  
Series Method ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Exact Analytic Solutions ◽  
Rosenau Equation ◽  
Physical Phenomena ◽  
Similarity Reductions

The Lie symmetry analysis is performed on the Rosenau equation which arises in modeling many physical phenomena. The similarity reductions and exact solutions are presented. Then the exact analytic solutions are considered by the power series method.

Lie symmetry analysis of the deformed KdV equation

2017 ◽  
Vol 31 (30) ◽  
pp. 1750275 ◽  
Author(s):  
Yehui Huang ◽  
Wei Li ◽  
Guo Wang ◽  
Xuelin Yong
Keyword(s):  
Kdv Equation ◽  
Classical Equation ◽  
Analytic Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
System Method ◽  
Exact Analytic Solutions ◽  
Similarity Reductions

The deformed KdV equation is a generalization of the classical equation that can describe the motion of the interaction between different solitary waves. In this paper, the Lie symmetry analysis is performed on the deformed KdV equation. The similarity reductions and exact solutions are obtained based on the optimal system method. The exact analytic solutions are considered by using the power series method. The conservation laws for the deformed KdV equation are presented. Finally, the analytic solutions are given and their dynamics are studied.

scholarly journals Symmetry Analysis and Exact Solutions to the Space-Dependent Coefficient PDEs in Finance

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hanze Liu
Keyword(s):  
Power Series ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Similarity Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Series Method ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Generalized Power Series

The variable-coefficients partial differential equations (vc-PDEs) in finance are investigated by Lie symmetry analysis and the generalized power series method. All of the geometric vector fields of the equations are obtained; the symmetry reductions and exact solutions to the equations are presented, including the exponentiated solutions and the similarity solutions. Furthermore, the exact analytic solutions are provided by the transformation technique and generalized power series method, which has shown that the combination of Lie symmetry analysis and the generalized power series method is a feasible approach to dealing with exact solutions to the variable-coefficients PDEs.

scholarly journals A Truncation Method for Solving the Time-Fractional Benjamin-Ono Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed R. Ali
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Power Series ◽  
Fractional Order ◽  
Nonlinear Ordinary Differential Equation ◽  
Lie Symmetry ◽  
Series Method ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Bo Equation

We deem the time-fractional Benjamin-Ono (BO) equation out of the Riemann–Liouville (RL) derivative by applying the Lie symmetry analysis (LSA). By first using prolongation theorem to investigate its similarity vectors and then using these generators to transform the time-fractional BO equation to a nonlinear ordinary differential equation (NLODE) of fractional order, we complete the solutions by utilizing the power series method (PSM).

scholarly journals Exact Solutions and Conservation Laws of the (3 + 1)-Dimensional B-Type Kadomstev–Petviashvili (BKP)-Boussinesq Equation

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 97 ◽  
Author(s):  
Ben Gao ◽  
Yao Zhang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Boussinesq Equation ◽  
Lie Symmetry ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Reduced Equations ◽  
Tanh Method ◽  
Similarity Reductions

In this paper, Lie symmetry analysis is presented for the (3 + 1)-dimensional BKP-Boussinesq equation, which seriously affects the dispersion relation and the phase shift. To start with, we derive the Lie point symmetry and construct the optimal system of one-dimensional subalgebras. Moreover, according to the optimal system, similarity reductions are investigated and we obtain exact solutions of reduced equations by means of the Tanh method. In the end, we establish conservation laws using Ibragimov’s approach.

Symmetry analysis and invariant solutions of (3 + 1)-dimensional Kadomtsev–Petviashvili equation

2018 ◽  
Vol 15 (08) ◽  
pp. 1850125 ◽  
Author(s):  
Vishakha Jadaun ◽  
Sachin Kumar
Keyword(s):  
Lie Algebra ◽  
Zeta Functions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Lie Symmetry Method ◽  
Petviashvili Equation ◽  
Symmetry Method ◽  
Similarity Reductions

Based on Lie symmetry analysis, we study nonlinear waves in fluid mechanics with strong spatial dispersion. The similarity reductions and exact solutions are obtained based on the optimal system and power series method. We obtain the infinitesimal generators, commutator table of Lie algebra, symmetry group and similarity reductions for the [Formula: see text]-dimensional Kadomtsev–Petviashvili equation. For different Lie algebra, Lie symmetry method reduces Kadomtsev–Petviashvili equation into various ordinary differential equations (ODEs). Some of the solutions of [Formula: see text]-dimensional Kadomtsev–Petviashvili equation are of the forms — traveling waves, Weierstrass’s elliptic and Zeta functions and exponential functions.

scholarly journals Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Expansion Method ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Similarity Reductions

Lie symmetry analysis is performed on a generalized two-dimensional nonlinear Kadomtsev-Petviashvili-modified equal width equation. The symmetries and adjoint representations for this equation are given and an optimal system of one-dimensional subalgebras is derived. The similarity reductions and exact solutions with the aid ofG′/G-expansion method are obtained based on the optimal systems of one-dimensional subalgebras. Finally conservation laws are constructed by using the multiplier method.

Group Invariant Solutions and Conservation Laws of the Fornberg– Whitham Equation

2014 ◽  
Vol 69 (8-9) ◽  
pp. 489-496 ◽  
Author(s):  
Mir Sajjad Hashemi ◽  
Ali Haji-Badali ◽  
Parisa Vafadar
Keyword(s):  
Exact Solutions ◽  
Reduction Method ◽  
Lie Symmetry ◽  
First Integrals ◽  
Invariant Solutions ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Whitham Equation

In this paper, we utilize the Lie symmetry analysis method to calculate new solutions for the Fornberg-Whitham equation (FWE). Applying a reduction method introduced by M. C. Nucci, exact solutions and first integrals of reduced ordinary differential equations (ODEs) are considered. Nonlinear self-adjointness of the FWE is proved and conserved vectors are computed

scholarly journals New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation

2021 ◽  
Vol 10 (1) ◽  
pp. 374-384
Author(s):  
Mustafa Inc ◽  
E. A. Az-Zo’bi ◽  
Adil Jhangeer ◽  
Hadi Rezazadeh ◽  
Muhammad Nasir Ali ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Solution Process ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Bright Solitons ◽  
Exact Analytic Solutions ◽  
Higher Dimensional ◽  
Non Local ◽  
Free Parameters ◽  
Ito Equation

Abstract In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are also described graphically while taking suitable values of free parameters. The applied algorithms are effective and convenient in handling the solution process for Ito equation that appears in many phenomena.

Sign in / Sign up

Export Citation Format

Share Document