In this paper the Galilean, scaling and translational self–similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite dimensional Grassmannian. The string equations found recently by non–scaling limit analysis of the one–matrix model are shown to correspond to the Galilean self–similarity condition for this hierarchy. We describe, in terms of the initial da...

In this paper we study to find parametric presentation of a surface family with common line curvature in 3-dimensional Galilean space. We obtain necessary and sufficient conditions for the curve be on surface. state examples visualize our results some torsion free curve.

The string equation appearing in the double scaling limit of the Hermitian one–matrix model, which corresponds to a Galilean self–similar condition for the KdV hierarchy, is reformulated as a scaling self–similar condition for the Ur–KdV hierarchy. A non–scaling limit analysis of the one–matrix model has led to the complexified NLS hierarchy and a string equation. We show that this corresponds ...

We consider a new D = 2 nonrelativistic classical mechanics model providing via the Noether theorem the (2 + 1)-Galilean symmetry algebra with two central charges: mass m and the coupling constant k of a Chern-Simons-like term. In this way we provide the dynamical interpretation of the second central charge of the (2 + 1)-dimensional Galilean algebra. We discuss also the interpretation of k as ...

Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics. Souriau's construction applied to the two-parameter central extension of the planar Galilei group lead to the " exotic " particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical mod...

We study the nonrelativistic limit of the N = 2 supersymmetric Chern-Simons matter system. We show that in addition to Galilean invariance the model admits a set of symmetries generated by fermionic charges, which can be interpreted as an extended Galilean supersymmetry. The system also possesses a hidden conformal invariance and then the full group of symmetries is the extended superconformal ...

We present a new theory of the four Galilean satellites Io, Europa, Ganymede and Callisto. This theory aims to deliver highly accurate ephemerides able to represent the Galilean satellites’ motion over several centuries. It is based on the numerical integration of elaborated equations of motion. This first paper describes and tests many usually neglected perturbations. We are then able to retai...

Galilean invariance is one of the key requirements of many physical models adopted in theoretical and computational mechanics. Spurred by recent research developments in shock hydrodynamics computations [13], a detailed analysis on the principle of Galilean invariance in the context of SUPG operators is presented. It was observed in [13] that lack of Galilean invariance can yield catastrophic i...

We study roughening interfaces with a constant slope that become self organized critical by a rule that is similar to that of invasion percolation. The transient and critical dynamical exponents show Galilean invariance. The activity along the interface exhibits nontrivial power law correlations in both space and time. The probability distribution of the activity pattern follows an algebraic re...

The apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed minkowskian. Matter made of solutions of Lorentz-invariant equations would feel a relativistic space-time even if the actual space-time had a quite different geometry (f.i. a galilean space-time). A typical example is provided by sine-Gordon solitons in a galilean world. A " sub-world " restricted to...