Results 61 to 70 of about 530,977 (309)

Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation

Mathematical Biosciences and Engineering, 2023
In this paper, a (2+1)-dimensional KdV4 equation is considered. We obtain Lie symmetries of this equation by utilizing Lie point symmetry analysis method, then use them to perform symmetry reductions.
Sixing Tao
doaj   +1 more source

Lie-point symmetries and nonlinear dynamical systems

Mathematical and Computer Modelling, 1997
Nonlinear symmetries of finite dimensional dynamical systems are related to nonlinear normal forms and center manifolds in the neighbourhood of a singular point. Certain abstract results can be used algorithmically to construct the normal forms and/or the center manifold up to a given order in the perturbation expansion.
G. Gaeta, G. Cicogna
openaire   +2 more sources

A Group Theoretical Identification of Integrable Equations in the Li\'enard Type Equation $\ddot{x}+f(x)\dot{x}+g(x) = 0$ : Part II: Equations having Maximal Lie Point Symmetries

, 2009
In this second of the set of two papers on Lie symmetry analysis of a class of Li\'enard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are smooth ...
Ibragimov N. H., Korn F. A., Lie S., M. Lakshmanan, M. Senthilvelan, P. S. Bindu, Prince G. E., S. N. Pandey   +7 more
core   +1 more source

Quantification and dosimetric impact of intra‐fractional bladder changes during CBCT‐guided online adaptive radiotherapy for pelvic cancer treatments

Journal of Applied Clinical Medical Physics, EarlyView.
Abstract Purpose This study quantitatively evaluates bladder changes and their dosimetric impact during the on‐couch adaptive process on a commercial CBCT‐based online adaptive radiotherapy (CT‐gART) platform. Methods Data from 183 fractions of ten patients receiving online ART for pelvic cancers were analyzed retrospectively.
Ingrid Valencia Lozano, Elizabeth Buss, Catherine S. Spina, David P. Horowitz, Lisa A. Kachnic, Michael Price, Yi‐Fang Wang, Reshma Munbodh   +7 more
wiley   +1 more source

Claustrum Volume Is Reduced in Multiple Sclerosis and Predicts Disability

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective The claustrum is a small, thin structure of predominantly gray matter with broad connectivity and enigmatic function. Little is known regarding the impact of claustrum pathology in multiple sclerosis (MS). Methods This study assessed whether claustrum volume was reduced in MS and whether reductions were associated with specific ...
Nicole Shelley, Bradley Judge, Dmitriy A. Yablonskiy, Robert T. Naismith, Matthew R. Brier, Anne H. Cross   +5 more
wiley   +1 more source

Lie symmetry analysis, Lie-Bäcklund symmetries, explicit solutions, and conservation laws of Drinfeld-Sokolov-Wilson system

Boundary Value Problems, 2017
The symmetry analysis method is used to study the Drinfeld-Sokolov-Wilson system. The Lie point symmetries of this system are obtained. An optimal system of one-dimensional subalgebras is derived by using Ibragimov’s method.
Yufeng Zhang, Zhonglong Zhao
doaj   +1 more source

Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation

International Journal of Differential Equations, 2023
In this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the time-fractional generalized foam drainage equation with the Riemann–Liouville derivative.
Maria Ihsane El Bahi, Khalid Hilal
doaj   +1 more source

Elasticity of Diametrically Compressed Microfabricated Woodpile Lattices

Advanced Engineering Materials, EarlyView.
Modulus–porosity relationship is derived for woodpile lattices with struts under diametrical compression. The formula presented here that Young's modulus is proportional to the square of the volume fraction E˜ρ2$E \sim \left(\rho\right)^{2}$ is shown to be consistent with computations and laboratory experiments on 3D‐printed samples.
Faezeh Shalchy, Atul Bhaskar
wiley   +1 more source

Symmetries of Ricci Flows [PDF]

arXiv, 2022
In the present work we find the Lie point symmetries of the Ricci flow on an $n$-dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this method to retrieve the Lie point symmetries of the Einstein equations -- seen as a "static" Ricci flow -- , and of
arxiv  

Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices

, 2006
This paper is mainly a review of the multi--Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results.
Collingwood D. H., Damianou P. A., Ibragimov N. H., Koszul J. L., Kupershmidt B., Lichnerowicz A., Manakov S., Moser J., Oevel W., Ovsiannikov L. V., PANTELIS A. DAMIANOU, Smirnov R. G., Weinstein A.   +12 more
core   +1 more source