相关论文: Comment on "A note on the construction of the Erma…

Contents: Introduction(3).The method of Ermakov(4).The method of Milne(7). Pinney's result(8).Lewis' results(8). The interpretation of Eliezer and Gray(14). The connection of the Ermakov invariant with N\"other's theorem(17). Possible…

In the paper Sci. Rep. 8, 8401 (2018), among other things, the Ermakov-Lewis invariant was constructed for the time dependent harmonic oscillator in Koopman-von Neumann mechanics. We point out that there is a simpler method that allows one…

Ermakov systems possessing Noether point symmetry are identified among the Ermakov systems that derive from a Lagrangian formalism and, the Ermakov invariant is shown to result from an associated symmetry of dynamical character. The Ermakov…

We show that a simple modification of the Lagrangian proposed by Padmanabhan in the paper [Mod. Phys. Lett. A 33, 1830005 (2018), arXiv:1712.07328] leads to the most general dynamical invariant in [Ray and Reid, Phys. Lett. A 71, 317…

We show that the recent results of \ [Int. J. Mod. Phys. D 25 (2016) 1650051] on the application of Lie/Noether symmetries in scalar field cosmology are well-known in the literature while the problem could have been solved easily under a…

In this work we study the Ermakov-Lewis invariants of the non-linear Gross-Pitaeviskii equation

We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found…

This is a short communication in reference to the comments in (arXiv: 1605.05147) of our paper in Int. J. Mod. Phys. D 25, 1650051 (2016). We have tried to answer to the comments or criticism in the paper.

These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.

Noether's problem is classical and very important problem in algebra. It is an intrinsically interesting problem in invariant theory, but with far reaching applications in the sutdy of moduli spaces, PI-algebras, and the Inverse problem of…

We prove that in the Ryabov paper an application of the geometric Kharlamov method to the Goryachev system yields noncommutative "new variables of separation" instead of the standard canonical variables of separation.

In this work we study the Ermakov-Lewis invariants of the Schrodinger equation continuous measurement.

We comment on the validity of Noether's theorem and on the conclusions of [J. Math. Phys. 61 (2020), no. 11, 113502].

We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painlev\'e equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V.…

It is shown that the results of ref [1] are consistent.

Reid's m'th-order generalized Ermakov systems of nonlinear coupling constant alpha are equivalent to an integrable Emden-Fowler equation. The standard Ermakov-Lewis invariant is discussed from this perspective, and a closed formula for the…

By using Lie symmetry methods, we identify a class of second order nonlinear ordinary differential equations invariant under at least one dimensional subgroup of the symmetry group of the Ermakov-Pinney equation. In this context, nonlinear…

The connection between the Equivalence Principle and Noether's theorem was discussed in S. Capozziello and C. Ferrara, Int. J. Geom. Meth. Mod. Phys. 21, 2440014 (2024). However, it is known that the Noether symmetry condition is…

Using older and recent results on the integrability of two-dimensional (2d) dynamical systems, we prove that the results obtained in a recent publication concerning the 2d generalized Ermakov system can be obtained as special cases of a…

The Comments are devoted to the recently published paper 'Modelling and nonclassical symmetry analysis of a complex porous media flow in a dilating channel' (Physica D. 481 (2025) 134834), in which a model describing an unsteady…