# SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems

## Related Articles

- BÃ¤cklund transformations for the Caudreyâ€“Doddâ€“Gibbonâ€“Sawadaâ€“Kotera equation and its Î»-modified equation. Chan, W. L.; Zheng, Yu-kun // Journal of Mathematical Physics;Sep89, Vol. 30 Issue 9, p2065
A Î»-modified equation for the Caudrey-Dodd-Gibbon-Sawada-Kotera equation is introduced. A new BÃ¤cklund transformation for this equation is derived from the invariance property of the scattering problem for the Caudrey-Dodd-Gibbon-Sawada-Kotera equation under a Cram transformation [Q. J....

- A new eight-vertex model with an infinite number of commensurate phases. Sen, Diptiman // Journal of Mathematical Physics;Dec88, Vol. 29 Issue 12, p2682
A symmetric eight-vertex model, containing four even vertices with reak weights and four odd vertices with imaginary weights, is found to exhibit an infinite number of commensurate phases. The phase diagram is conjectured to be a complete devilâ€™s staircase similar to that of certain...

- Noise-induced transitions vs. noise-induced phase transitions. Toral, Raúl // AIP Conference Proceedings;3/24/2011, Vol. 1332 Issue 1, p145
I will briefly review the field of noise-induced phase transitions, emphasizing the main differences with the phase-induced transitions and showing that they appear in different systems. I will show that a noise-induced transition can disappear after a suitable change of variables and I will...

- Critical properties of the two dimensional fully frustrated XY model. Sugimoto, K.; Ebina, K. // AIP Conference Proceedings;2000, Vol. 519 Issue 1, p374
Phase transitions of the two-dimensional fully frustrated XY model (2DFFXY model) have been studied extensively in recent years [1]. It is well known that the ordinary XY model has the O(2) symmetry which is related to the phase angle of spins. The 2DFFXY model bears also a discrete Z[sub 2]...

- Phase Transitions Characterized by Polarization Vector and Rotation Pseudovector in Crystals of Arbitrary Point Symmetry. Adamov, V. A.; Darinskiı, B. M.; Shalimov, V. V. // Crystallography Reports;Mar2001, Vol. 46 Issue 2, p256
A thermodynamic theory of phase transitions in crystals characterized by the rotational and polarization components has been developed. A list of phase transitions accompanied by the change of the group to a subgroup is compiled for crystals whose thermodynamic potential can be represented by a...

- Orientational states of C[sub 60] molecule in crystals. Aksenov, V. L.; Shakhmatov, V. S.; Osip’yan, Yu. A. // Journal of Experimental & Theoretical Physics;Mar98, Vol. 86 Issue 3, p591
Local symmetry of orientational states of the C[sub 60] molecule in crystals has been investigated. It was shown that the various orientational phase transitions in different crystals are related to different orientational orbits. The model of orientational phase transitions based on a sequence...

- Optical and X-ray Studies of the Structural Phase Transition in Cryolite (NH[sub 4])[sub 3]GaF[sub 6]. Mel’nikova, S. V.; Misyul’, S. V.; Bovina, A. F.; Afanas’ev, M. L. // Physics of the Solid State;Aug2001, Vol. 43 Issue 8, p1594
Optical polarization and x-ray diffraction studies of powders and single-crystal plates of different cuts of an (NH[sub 4])[sub 3]GaF[sub 6] crystal are carried out in a broad temperature range, including the phase transition point. 1 The following sequence of symmetry changes is found to occur:...

- On the possibility of spontaneous breaking the ideal crystal symmetry. Myasnikov, E. N.; Myasnikova, A. E. // AIP Conference Proceedings;2001, Vol. 554 Issue 1, p315
On the base of the single-particle distribution function obtained for fermions in systems where their autolocalization is possible it is shown that there exist some critical temperature T[sub c] such that macroscopic number of carriers from partially or completely filled band merge into...

- Exact solutions for wave equations of two-layered media with smooth transition. Bluman, George; Kumei, Sukeyuki // Journal of Mathematical Physics;Jan1988, Vol. 29 Issue 1, p86
The wave equation c2(x)uxx-utt=0 is solved for wave speeds c(x) corresponding to two-layered media with smooth transition from layer to layer. The wave speed c(x) has four free parameters to fit a given medium. Solutions are constructed from invariant solutions of a related system of first-order...