A discrete linearizability test based on multiscale analysis

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A_1, A_2 and A_3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A_3 C-integrability conditions can be linearized by a Mobius transformation

A discrete linearizability test based on multiscale analysis

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A1, A2 and A3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A3 C-integrability conditions can be linearized by a Möbius transformation

Multiscale expansion and integrability properties of the lattice potential KdV equation

We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schroedinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007 Conferenc

On the Integrability of the Discrete Nonlinear Schroedinger Equation

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a reductive perturbation technique to show an obstruction to its integrability.Comment: 4 pages, accepted in EP

Classification of integrable discrete Klein-Gordon models

The Lie algebraic integrability test is applied to the problem of classification of integrable Klein-Gordon type equations on quad-graphs. The list of equations passing the test is presented containing several well-known integrable models. A new integrable example is found, its higher symmetry is presented.Comment: 12 pages, submitted to Physica Script

Point Symmetries of Generalized Toda Field Theories

A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point symmetries of these theories are found for an infinite, semi-infinite and finite number of fields. Special attention is accorded to conformal invariance and its breaking.Comment: 25 pages, no figures, Latex fil

Radiation and Dust Sensor for Mars Environmental Dynamic Analyzer Onboard M2020 Rover

32 pags., 26 figs., 3 tabs. -- This article belongs to the Section Remote SensorsThe Radiation and Dust Sensor is one of six sensors of the Mars Environmental Dynamics Analyzer onboard the Perseverance rover from the Mars 2020 NASA mission. Its primary goal is to characterize the airbone dust in the Mars atmosphere, inferring its concentration, shape and optical properties. Thanks to its geometry, the sensor will be capable of studying dust-lifting processes with a high temporal resolution and high spatial coverage. Thanks to its multiwavelength design, it will characterize the solar spectrum from Mars' surface. The present work describes the sensor design from the scientific and technical requirements, the qualification processes to demonstrate its endurance on Mars' surface, the calibration activities to demonstrate its performance, and its validation campaign in a representative Mars analog. As a result of this process, we obtained a very compact sensor, fully digital, with a mass below 1 kg and exceptional power consumption and data budget features.This work has been funded with the help of the Spanish National Research, Development and Innovation Program, through the grants RTI2018-099825-B-C31, ESP2016-80320-C2-1-R and ESP2014-54256-C4-3-R. DT acknowledges the financial support from the Comunidad de Madrid for an “Atracción de Talento Investigador” grant (2018-T2/TIC10500). ASL is supported by Grant PID2019-109467GB-I00 funded by MCIN/AEI/10.13039/501100011033/ and by Grupos Gobierno Vasco IT1366-19. The US co-authors performed their work under sponsorship from NASA’s Mars 2020 project, from the Game Changing Development program within the Space Technology Mission Directorate, and from the Human Exploration and Operations Directorate.Peer reviewe