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 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.

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 Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis

2019 ◽  
Vol 27 (2) ◽  
pp. 171-185 ◽  
Author(s):  
Astha Chauhan ◽  
Rajan Arora
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Analytic Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Power Series Method ◽  
Lie Symmetry Method ◽  
Liouville Fractional Derivative ◽  
Symmetry Generators ◽  
Symmetry Method

AbstractIn this work, the fractional Lie symmetry method is applied for symmetry analysis of time fractional Kupershmidt equation. Using the Lie symmetry method, the symmetry generators for time fractional Kupershmidt equation are obtained with Riemann-Liouville fractional derivative. With the help of symmetry generators, the fractional partial differential equation is reduced into the fractional ordinary differential equation using Erdélyi-Kober fractional differential operator. The conservation laws are determined for the time fractional Kupershmidt equation with the help of new conservation theorem and fractional Noether operators. The explicit analytic solutions of fractional Kupershmidt equation are obtained using the power series method. Also, the convergence of the power series solutions is discussed by using the implicit function theorem.

scholarly journals Lie symmetry analysis and conservation law for the equation arising from higher order Broer-Kaup equation

2019 ◽  
Vol 17 (1) ◽  
pp. 1045-1054
Author(s):  
Hengtai Wang ◽  
Huiwen Chen ◽  
Zigen Ouyang ◽  
Fubin Li
Keyword(s):  
Lie Group ◽  
Conservation Law ◽  
Higher Order ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Group Method ◽  
Lie Symmetry Analysis ◽  
Lie Group Method ◽  
Similarity Reductions

Abstract In this paper, Lie symmetry analysis is performed for the equation derived from $(2+1)$-dimensional higher order Broer-Kaup equation. Meanwhile, the optimal system and similarity reductions based on the Lie group method are obtained. Furthermore, the conservation law is studied via the Ibragimov’s method.

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.

scholarly journals Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Baoyong Guo ◽  
Huanhe Dong ◽  
Yong Fang
Keyword(s):  
Conservation Laws ◽  
Differential Operators ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Symmetry Groups ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Reduced Equations ◽  
Liouville Fractional Derivative ◽  
Similarity Reductions

In this paper, the time-fractional Fujimoto–Watanabe equation is investigated using the Riemann–Liouville fractional derivative. Symmetry groups and similarity reductions are obtained by virtue of the Lie symmetry analysis approach. Meanwhile, the time-fractional Fujimoto–Watanabe equation is transformed into three kinds of reduced equations and the third of which is based on Erdélyi–Kober fractional integro-differential operators. Furthermore, the conservation laws are also acquired by Ibragimov’s theory.

Sign in / Sign up

Export Citation Format

Share Document