Results 131 to 140 of about 26,049 (163)
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A Lie Symmetry Analysis of the Caldeira-Leggett Model
Open Systems & Information Dynamics, 2010An 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 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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Lie symmetry analysis of a variable coefficient Calogero–Degasperis equation
Physica Scripta, 2018Abstract We consider a general class of variable coefficient Calogero–Degasperis equations. The complete Lie group classification is performed with the aid of the appropriate equivalence group. Lie symmetries are used to derive a number of reductions by constructing the corresponding optimal lists of one-dimensional subalgebras of the
Sophocleous, Christodoulos +3 more
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Lie Symmetry Analysis and Exact Solutions for the Extended mKdV Equation
Acta Applicandae Mathematicae, 2008This paper concerns solutions of an extended mKdV equation of the form \[ u_t +a_1 u_{xxx} + a_2 u_x +a_3 u u_x + a_4 u^2 u_x = 0, \] where \(u = u(x,t)\) is an unknown function and the parameters \(a_i\) are real numbers with \(a_1 a_4 \neq 0\). Its exact solutions are obtained by using the method of Lie symmetry analysis as well as the method of ...
Liu, Hanze, Li, Jibin
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Lie Symmetry Analysis for the Degasperis-Procesi Equation Based on Maple
2012In this paper, the Lie symmetry analysis is performed for the Degasperis-Procesi equation. By taking the package Desolv in maple and Lie group method, the exact solutions from the symmetry transformations are provided. Such exact explicit solutions are important in both applications and the theory of nonlinear science.
Qing Wang, Tao Wang
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