scholarly journals New conservation laws and exact solutions of the special case of the fifth-order KdV equation

2021 ◽  
Author(s):  
Arzu Akbulut ◽  
Melike Kaplan ◽  
Mohammed K.A. Kaabar
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Fifth Order ◽  
Special Case

Group analysis, exact solutions and conservation laws of a generalized fifth order KdV equation

2016 ◽  
Vol 86 ◽  
pp. 8-15 ◽  
Author(s):  
Gangwei Wang ◽  
Abdul H. Kara ◽  
Kamran Fakhar ◽  
Jose Vega-Guzman ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Group Analysis ◽  
Fifth Order

scholarly journals Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Li-hua Zhang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Time Dependent ◽  
Group Method ◽  
New Exact Solutions ◽  
Petviashvili Equation ◽  
The Kdv Equation ◽  
Special Case

The (2 + 1)-dimensional Kadomtsev-Petviashvili equation with time-dependent coefficients is investigated. By means of the Lie group method, we first obtain several geometric symmetries for the equation in terms of coefficient functions and arbitrary functions oft. Based on the obtained symmetries, many nontrivial and time-dependent conservation laws for the equation are obtained with the help of Ibragimov’s new conservation theorem. Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. At the same time, many new exact solutions are derived such as soliton and soliton-like solutions and algebraically explicit analytical solutions.

scholarly journals Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion

2020 ◽  
Vol 13 (10) ◽  
pp. 2691-2701
Author(s):  
María-Santos Bruzón ◽  
◽  
Elena Recio ◽  
Tamara-María Garrido ◽  
Rafael de la Rosa
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Lie Symmetries

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.

SYMMETRY ANALYSIS FOR A SEVENTH-ORDER GENERALIZED KdV EQUATION AND ITS FRACTIONAL VERSION IN FLUID MECHANICS

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050044 ◽  
Author(s):  
GANGWEI WANG ◽  
YIXING LIU ◽  
YANBIN WU ◽  
XING SU
Keyword(s):  
Fluid Mechanics ◽  
Conservation Laws ◽  
Kdv Equation ◽  
Differential Invariants ◽  
Potential Equation ◽  
Generalized Kdv Equation ◽  
Seventh Order ◽  
Special Case ◽  
Symmetry Method ◽  
Similarity Reductions

KdV types of equations play an important role in many fields. In this paper, we study a seventh-order generalized KdV equation and its fractional version in fluid mechanics using symmetry. From symmetry, the corresponding vectors, symmetry reduction and conservation laws are derived. Potential equation is also analyzed with regard to the symmetry method. Based on the symmetry, similarity reductions and conservation laws are also presented. Subsequently, the fractional version of the seventh-order KdV equation is discussed. Finally, differential invariants are constructed for the special case.

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