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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 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 the Heisenberg equation
Communications in Nonlinear Science and Numerical Simulation, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Zhonglong, Han, Bo
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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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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 ...
Naicker, V., Petruccione, F.
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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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Lie symmetry classification analysis for nonlinear coupled diffusion
Journal of Physics A: Mathematical and General, 1998Summary: The group properties of the \((1+1)\)-dimensional matrix diffusion equation of the form \(\partial y/\partial t= \partial\{\Lambda(y)\partial y/\partial x\}/\partial x\) with respect to point symmetries are given. It is shown that in particular cases the group properties of this equation are similar to those of the corresponding scalar ...
Baikov, V. A. +2 more
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Lie symmetry analysis of a variable coefficient Calogero–Degasperis equation
Physica Scripta, 2018We 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 Lie symmetry algebras ...
Sophocleous, Christodoulos +3 more
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Lie symmetry analysis for cubic–quartic nonlinear Schrödinger's equation
Optik, 2018Abstract This paper carries out Lie symmetry analysis of the cubic–quartic nonlinear Schrodinger's equation that models soliton dynamics whenever group velocity dispersion is negligibly small. The results are presented for Kerr and power laws of nonlinearity.
Anupma Bansal +3 more
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