Group analysis of KdV equation with time dependent coefficients

2010 ◽  
Vol 216 (12) ◽  
pp. 3761-3771 ◽  
Author(s):  
A.G. Johnpillai ◽  
C.M. Khalique
Keyword(s):  
Kdv Equation ◽  
Group Analysis ◽  
Time Dependent

scholarly journals Lie Group Analysis of a Forced KdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Motlatsi Molati ◽  
Chaudry Masood Khalique
Keyword(s):  
Mathematical Model ◽  
Shallow Water ◽  
Lie Group ◽  
Kdv Equation ◽  
Group Analysis ◽  
Time Dependent ◽  
Analysis Approach ◽  
External Forcing ◽  
Lie Group Analysis ◽  
Forcing Term

The Korteweg-de Vries (KdV) equation considered in this work contains a forcing term and is referred to as forced KdV equation in the sequel. This equation has been investigated recently as a mathematical model for waves on shallow water surfaces under the influence of external forcing. We employ the Lie group analysis approach to specify the time-dependent forcing term.

Symmetry operators and exact solutions of a type of time-fractional Burgers–KdV equation

2019 ◽  
Vol 16 (02) ◽  
pp. 1950032 ◽  
Author(s):  
Azadeh Naderifard ◽  
S. Reza Hejazi ◽  
Elham Dastranj ◽  
Ahmad Motamednezhad
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Vector Fields ◽  
Kdv Equation ◽  
Group Analysis ◽  
Invariant Subspaces ◽  
Similarity Solutions ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Symmetry Operators

In this paper, group analysis of the fourth-order time-fractional Burgers–Korteweg–de Vries (KdV) equation is considered. Geometric vector fields of Lie point symmetries of the equation are investigated and the corresponding optimal system is found. Similarity solutions of the equation are presented by using the obtained optimal system. Finally, a useful method called invariant subspaces is applied in order to find another solutions.

Solutions of the generalized KdV equation with time-dependent damping and dispersion

2010 ◽  
Vol 216 (4) ◽  
pp. 1029-1035 ◽  
Author(s):  
Yang Yang ◽  
Zhao-ling Tao ◽  
Francis R. Austin
Keyword(s):  
Kdv Equation ◽  
Time Dependent ◽  
Generalized Kdv Equation

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny–Lin equation

2017 ◽  
Vol 14 (12) ◽  
pp. 1750170 ◽  
Author(s):  
Saeede Rashidi ◽  
S. Reza Hejazi
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Group Analysis ◽  
Navier Stokes ◽  
Kawahara Equation ◽  
Navier Stokes Equation ◽  
Invariance Properties ◽  
Fractional Differential ◽  
Fifth Order ◽  
Sivashinsky Equation

This paper investigates the invariance properties of the time fractional Benny–Lin equation with Riemann–Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto–Sivashinsky equation and Navier–Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny–Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

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