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A Lie Symmetry Analysis of the Caldeira-Leggett Model
Open Systems & Information Dynamics, 2010 An important model in the theory of open quantum systems is the Caldeira-Leggett quantum Brownian motion model for the behaviour of a massive quantum particle weakly interacting with a bath of harmonic oscillators. The model is formulated in terms of a (1 + 2) dimensional partial differential equation (PDE) for the reduced density matrix of the ...
Viroshan Naicker, Francesco Petruccione
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Lie symmetry analysis of the time fractional KdV-type equation
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yujian Ye, Shoufeng Shen
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Lie symmetry analysis of the Heisenberg equation
Communications in Nonlinear Science and Numerical Simulation, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhonglong Zhao, Bo Han 0007
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Lie Symmetry Analysis and Exact Solutions of Generalized Fractional Zakharov-Kuznetsov Equations
Symmetry, 2019 This paper considers the Lie symmetry analysis of a class of fractional Zakharov-Kuznetsov equations. We systematically show the procedure to obtain the Lie point symmetries for the equation.
Changzhao Li
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Lie Symmetry Analysis of Differential Equations in Finance
Nonlinear Dynamics, 1998The Black-Schole equation \(u_t+\frac{1}{2} A^2x^2u_{xx}+ Bxu_x-Cu=0\) and Jacobs-Jones equation \(u_t=\frac{1}{2} A^2x^2u_{xx}+ ABCxyu_{xy}+ \frac{1}{2}B^2y^2u_{yy} +(Dx\ln\frac{y}{x}- Ex^{3/2})u_x+ (Fy\ln\frac{G}{y}- Hyx^{1/2})u_y-xu\) are investigated in this paper.
Gazizov, R. K., Ibragimov, N. H.
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Lie symmetry analysis of Burgers‐type systems
Mathematical Methods in the Applied Sciences, 2017Lie group classification for 2 Burgers‐type systems is obtained. Systems contain 2 arbitrary elements that depend on the 2 dependent variables. Equivalence transformations for the systems are derived. Examples of nonclassical reductions are given. A Hopf‐Cole–type mapping that linearizes a nonlinear system is presented.
Kontogiorgis, Stavros +3 more
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Lie and Noether symmetry analysis in Brans–Dicke cosmology
Modern Physics Letters A, 2018This paper is aimed to study the group invariant solutions of the evolution equations in Brans–Dicke cosmology. In this context, we have considered the flat homogeneous Brans–Dicke (BD) scalar field in the background of flat homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model and have used Lie and Noether symmetry ...
Dutta, Sourav, Mondal, Santu
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Lie symmetry analysis of the deformed KdV equation
Modern Physics Letters B, 2017The 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.
Yehui Huang +3 more
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Lie symmetry analysis of the quantum Zakharov equations
Physica Scripta, 2007The Lie point symmetries of the one-dimensional quantum Zakharov (qZ) system of equations are considered, which is a general model to describe the coupling between the Langmuir and the ion-acoustic waves in a quantum setting. It is demonstrated that the Lie symmetries of the qZ system are exactly similar to those of the classical Zakharov equations ...
Xiao-Yan Tang, Padma Kant Shukla
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USE OF LIE SYMMETRIES AND THE PAINLEVÉ ANALYSIS IN COSMOLOGY
Quaestiones Mathematicae, 1996Abstract Two techniques for the analysis of differential equations, the Lie method of extended groups and the Painleve analysis, are reviewed. The implications for integrability in the case of the existence of symmetries in the former or the possession of the Painleve property in the latter are explored. By way of an example an equation which arises in
P. G.L. Leach, K. S. Govinder
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