Integrability Test for Discrete Equations via Generalized Symmetries

AIP Conference Proceedings 10/2010; 1323. DOI: 10.1063/1.3537849
Source: arXiv


In this article we present some integrability conditions for partial
difference equations obtained using the formal symmetries approach. We apply
them to find integrable partial difference equations contained in a class of
equations obtained by the multiple scale analysis of the general multilinear
dispersive difference equation defined on the square.

Download full-text


Available from: Decio Levi, Oct 12, 2015
10 Reads
  • Source
    • "Fortunately, more arguments do exist. First, Levi and Yamilov [10] have shown that (2) with c 2 = 1/2 admits a five-point generalized symmetry, a property usually associated with integrability. Moreover Viallet [11] has computed the algebraic entropy [12] of both systems and shown that it is zero, which constitutes another indication of integrability. "
    [Show abstract] [Hide abstract]
    ABSTRACT: We examine two lattice equations, obtained through the application of multiscale perturbative analysis, from the point of view of integrability. We show that both equations are integrable and related to the discrete sine-Gordon. We compute the limit of both systems whereby they become linearizable, obtaining the discrete Liouville equation and a linearizable lattice system recently proposed by Hydon and Viallet. We present the explicit solution of the latter.
    Journal of Physics A Mathematical and Theoretical 12/2010; 44(3):032002. DOI:10.1088/1751-8113/44/3/032002 · 1.58 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: An agent-based model of farmers' crop and best management practice (BMP) decisions is developed and linked to a hydrologic-agronomic model of a watershed, to examine farmer behavior, and the attendant effects on stream nitrate load, under the influence of markets for conventional crops, carbon allowances, and a second-generation biofuel crop. The agent-based approach introduces interactions among farmers about new technologies and market opportunities, and includes the updating of forecast expectations and uncertainties using Bayesian inference. The model is applied to a semi-hypothetical example case of farmers in the Salt Creek Watershed in Central Illinois, and a sensitivity analysis is performed to effect a first-order assessment of the plausibility of the results. The results show that the most influential factors affecting farmers' decisions are crop prices, production costs, and yields. The results also show that different farmer behavioral profiles can lead to different predictions of farmer decisions. The farmers who are predicted to be more likely to adopt new practices are those who interact more with other farmers, are less risk averse, quick to adjust their expectations, and slow to reduce their forecast confidence. The decisions of farmers have direct water quality consequences, especially those pertaining to the adoption of the second-generation biofuel crop, which are estimated to lead to reductions in stream nitrate load. The results, though empirically untested, appear plausible and consistent with general farmer behavior. The results demonstrate the usefulness of the coupled agent-based and hydrologic-agronomic models for normative research on watershed management on the water-energy nexus.
    Water Resources Research 09/2011; 47(9). DOI:10.1029/2011WR010399 · 3.55 Impact Factor