Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation

2017 ◽  
Vol 72 (3) ◽  
pp. 261-267 ◽  
Author(s):  
Zhi-Yong Zhang ◽  
Kai-Hua Ma
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Series Solution ◽  
Power Series Solution ◽  
One Dimensional ◽  
Symmetry Classification ◽  
Symmetry Operators ◽  
Foam Drainage Equation ◽  
Foam Drainage

AbstractWe perform a complete Lie point symmetry classification of the generalised foam-drainage equation and then construct an optimal system of one-dimensional subalgebra of the admitted symmetry operators and use them to reduce the equations under study. A power series solution of the reduced equation is constructed. Moreover, we find all multipliers of the equations and apply them to construct conservation laws.

The generalized convective Cahn–Hilliard equation: Symmetry classification, power series solutions and dynamical behavior

2019 ◽  
Vol 31 (02) ◽  
pp. 2050024
Author(s):  
Zhi-Yong Zhang ◽  
Kai-Hua Ma ◽  
Li-Sheng Zhang
Keyword(s):  
Power Series ◽  
Critical Points ◽  
Driving Force ◽  
Series Solution ◽  
Dynamical Behavior ◽  
Compressive Force ◽  
Power Series Solution ◽  
Symmetry Classification ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

We first perform a complete Lie symmetry classification of the generalized convective Cahn–Hilliard equation. Then using the obtained symmetries, we mainly study the convective Cahn–Hilliard equation, of which a new power series solution is constructed. In particular for the crystal surface growth processes, the truncated series solution shows that the surface structures include peaks and valleys, and can exhibit different evolution trends with the driving force varying from compressive force to tensile force. Moreover, there exist several critical points for the driving force, where the surface configurations take the jump changes and show different features on the both sides of such critical points. According to the effects of driving forces, we analyze the dynamical features of crystal growth.

Time Fractional Third-Order Evolution Equation: Symmetry Analysis, Explicit Solutions, and Conservation Laws

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Dumitru Baleanu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Aliyu Isa Aliyu
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Series Solution ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equation ◽  
Symmetry Analysis ◽  
Power Series Solution ◽  
Lie Symmetry Analysis ◽  
Third Order ◽  
Contour Plots

In this work, Lie symmetry analysis for the time fractional third-order evolution (TOE) equation with Riemann–Liouville (RL) derivative is analyzed. We transform the time fractional TOE equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in Erdelyi–Kober (EK) sense. We obtain a kind of an explicit power series solution for the governing equation based on the power series theory. Using Ibragimov's nonlocal conservation method to time fractional partial differential equations (FPDEs), we compute conservation laws (CLs) for the TOE equation. Two dimensional (2D), three-dimensional (3D), and contour plots for the explicit power series solution are presented.

Optimal algebra and power series solution of fractional Black-Scholes pricing model

2021 ◽  
Vol 25 (8) ◽  
pp. 6075-6082
Author(s):  
Hemanta Mandal ◽  
B. Bira ◽  
D. Zeidan
Keyword(s):  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Pricing Model ◽  
Black Scholes

An analytical solution of the Gibbs–Dehem equation in multicomponent systems

1970 ◽  
Vol 48 (5) ◽  
pp. 752-763 ◽  
Author(s):  
A. D. Pelton
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Multicomponent Systems ◽  
Duhem Equation ◽  
Number Of Components ◽  
Analytical Power

A general analytical power-series solution of the Gibbs–Duhem equation in multicomponent systems of any number of components has been developed. The simplicity and usefulness of the solution is made possible through the choice of a special set of composition variables.

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