64 research outputs found
Energy Content of Colliding Plane Waves using Approximate Noether Symmetries
This paper is devoted to study the energy content of colliding plane waves
using approximate Noether symmetries. For this purpose, we use approximate Lie
symmetry method of Lagrangian for differential equations. We formulate the
first-order perturbed Lagrangian for colliding plane electromagnetic and
gravitational waves. It is shown that in both cases, there does not existComment: 18 pages, accepted for publication in Brazilian J Physic
A unified approach to Poisson-Hopf deformations of Lie-Hamilton systems based on sl(2)
Producción CientíficaBased on a recently developed procedure to construct Poisson-Hopf deformations of Lie–Hamilton systems, a novel unified approach to nonequivalent deformations of Lie–Hamilton systems on the real plane with a Vessiot–Guldberg Lie algebra isomorphic to sl(2) is proposed. This, in particular, allows us to define a notion of Poisson–Hopf systems in dependence of a
parameterized family of Poisson algebra representations. Such an approach is explicitly illustrated by applying it to the three non-diffeomorphic classes of sl(2) Lie–Hamilton systems. Our results cover deformations of the Ermakov system, Milne–Pinney, Kummer–Schwarz and several Riccati equations as well as of the harmonic oscillator (all of them with t-dependent coefficients). Furthermore t-independent constants of motion are given as well. Our methods can be employed to generate other Lie–Hamilton systems and their deformations for other Vessiot–Guldberg Lie algebras and their deformations
On the solutions and conservation laws of the ( 1 + 1 ) -dimensional higher-order Broer-Kaup system
Lie group analysis and similarity solutions for hydro-magnetic Maxwell fluid through a porous medium
Symmetry analysis and optimal systems of generalized Chaplygin gas equations with a source term
Invariant solutions of one‐dimensional equations of two‐temperature relaxation gas dynamics
Stationary solution of the nonlinear Schrödinger's equation with log law nonlinearity by Lie symmetry analysis
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