Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges.Comment: Talk given at the Workshop "Nonlinear Physics: Theory and Experiment. V", Gallipoli (Lecce, Italy), 12-21 June, 200

Dressing chain for the acoustic spectral problem

The iterations are studied of the Darboux transformation for the generalized Schroedinger operator. The applications to the Dym and Camassa-Holm equations are considered.Comment: 16 pages, 6 eps figure

Gauge-invariant description of some (2+1)-dimensional integrable nonlinear evolution equations

New manifestly gauge-invariant forms of two-dimensional generalized dispersive long-wave and Nizhnik-Veselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous two-dimensional generalization of dispersive long-wave system of equations, Nizhnik-Veselov-Novikov and modified Nizhnik-Veselov-Novikov equations and other known and new integrable nonlinear equations arise. Miura-type transformations between nonlinear equations in different gauges are considered.Comment: 13 pages, LaTeX, no figure

Functional representations of integrable hierarchies

We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which `functional representations' of particular hierarchies (like KP, discrete KP, mKP, AKNS), i.e. formulations in terms of functional equations, are systematically and quite easily obtained. The formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative (typically matrix) algebra. The obtained functional representations can be understood as `noncommutative' analogs of `Fay identities' for the KP hierarchy.Comment: 21 pages, version 2: equations (3.28) and (4.11) adde

An AGAMOUS-related MADS-box gene, XAL1 (AGL12), regulates root meristem cell proliferation and flowering transition in Arabidopsis

11 pages, 5 figures, 1 table.-- PMID: 18203871 [PubMed].-- PMCID: PMC2259045.-- Supplementary information available at: http://www.plantphysiol.org/cgi/content/full/pp.107.108647/DC1MADS-box genes are key components of the networks that control the transition to flowering and flower development, but their role in vegetative development is poorly understood. This article shows that the sister gene of the AGAMOUS (AG) clade, AGL12, has an important role in root development as well as in flowering transition. We isolated three mutant alleles for AGL12, which is renamed here as XAANTAL1 (XAL1): Two alleles, xal1-1 and xal1-2, are in Columbia ecotype and xal1-3 is in Landsberg erecta ecotype. All alleles have a short-root phenotype with a smaller meristem, lower rate of cell production, and abnormal root apical meristem organization. Interestingly, we also encountered a significantly longer cell cycle in the strongest xal1 alleles with respect to wild-type plants. Expression analyses confirmed the presence of XAL1 transcripts in roots, particularly in the phloem. Moreover, XAL1beta-glucuronidase expression was specifically up-regulated by auxins in this tissue. In addition, mRNA in situ hybridization showed that XAL1 transcripts were also found in leaves and floral meristems of wild-type plants. This expression correlates with the late-flowering phenotypes of the xal1 mutants grown under long days. Transcript expression analysis suggests that XAL1 is an upstream regulator of SOC, FLOWERING LOCUS T, and LFY. We propose that XAL1 may have similar roles in both root and aerial meristems that could explain the xal1 late-flowering phenotype.This work was supported by Consejo Nacional de Ciencia y Tecnología (CONACYT), México (grant nos. CO1.41848/A–1, CO1.0538/A–1, and CO1.0435.B–1); Dirección General de Asuntos del Personal Académico (DGAPA)-Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (PAPIIT), Universidad Nacional Autónoma de México (UNAM; grant nos. IN230002 and IX207104); and the University of California-MEXUS ECO IE 271 to E.R.A.-B. R.T.-L. was a recipient of CONACYT and DGAPA-PAPIIT-UNAM fellowships (no. IX225304). J.G.D. was supported by DGAPA-PAPIIT-UNAM (grant nos. IN210202 and IN225906) and CONACYT (grant no. 49267).Peer reviewe