We present a collective coordinate approximation to model the dynamics of two interacting nonlinear Schrödinger (NLS) solitons. We discuss the accuracy of this approximation by comparing our results with those of the full numerical simulations and find that the approximation is remarkably accurate when the solitons are some distance apart, and quite reasonable also during their interaction. arXiv:1308.4072v2 [hep-th]

This paper presents a comparison of the predictive capability of three hydrological models, and a mean ensemble of these models, in a heavily influenced catchment in Peninsular India: GWAVA (Global Water AVailability Assessment) model, SWAT (Soil Water Assessment Tool) and VIC (Variable Infiltration Capacity) model. The performance of the three models and their ensemble were investigated in five sub-catchments in the upstream reaches of the Cauvery river catchment. Model performances for monthly streamflow simulations from 1983–2005 were analysed using Nash-Sutcliffe efficiency, Kling-Gupta efficiency and percent bias. The predictive capability for each model was compared, and the ability to accurately represent key catchment hydrological processes is discussed. This highlighted the importance of an accurate spatial representation of precipitation for input into hydrological models, and that comprehensive reservoir functionality is paramount to obtaining good results in this region. The performance of the mean ensemble was analysed to determine whether the application of a multi-model ensemble approach can be useful in overcoming the uncertainties associated with individual models. It was demonstrated that the ensemble mean has a better predictive ability in catchments with reservoirs than the individual models, with Nash-Sutcliffe values between 0.49 and 0.92. Therefore, utilising multiple models could be a suitable methodology to offset uncertainty in input data and poor reservoir operation functionality within individual models.

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There has been renewed interest in the performance, functionality, and sustainability of traditional small-scale storage interventions (check dams, farm bunds and tanks) used within semi-arid regions for the improvement of local water security and landscape preservation. The Central Groundwater Board of India is encouraging the construction of such interventions for the alleviation of water scarcity and to improve groundwater recharge. It is important for water resource management to understand the hydrological effect of these interventions at the basin scale. The quantification of small-scale interventions in hydrological modelling is often neglected, especially in large-scale modelling activities, as data availability is low and their hydrological functioning is uncertain. A version of the Global Water Availability Assessment (GWAVA) water resources model was developed to assess the impact of interventions on the water balance of the Cauvery Basin and two smaller sub-catchments. Model results demonstrate that farm bunds appear to have a negligible effect on the average annual simulated streamflow at the outlets of the two sub-catchments and the basin, whereas tanks and check dams have a more significant and time varying effect. The open water surface of the interventions contributed to an increase in evaporation losses across the catchment. The change in simulated groundwater storage with the inclusion of interventions was not as significant as catchment-scale literature and field studies suggest. The model adaption used in this study provides a step-change in the conceptualisation and quantification of the consequences of small-scale storage interventions in large- or basin-scale hydrological models.

Abstract:We investigate the validity of collective coordinate approximations to the scattering of two solitons in several classes of (1+1) dimensional field theory models. We consider models which are deformations of the sine-Gordon (SG) or the nonlinear Schrödinger (NLS) model which posses soliton solutions (which are topological (SG) or non-topological (NLS)). Our deformations preserve their topology (SG), but change their integrability properties, either completely or partially (models become 'quasi-integrable').As the collective coordinate approximation does not allow for the radiation of energy out of a system we look, in some detail, at how the approximation fares in models which are 'quasi-integrable' and therefore have asymptotically conserved charges (i.e. charges Q(t) for which Q(t → −∞) = Q(t → ∞)).We find that our collective coordinate approximation, based on geodesic motion etc, works amazingly well in all cases where it is expected to work. This is true for the physical properties of the solitons and even for their quasi-conserved (or not) charges. The only time the approximation is not very reliable (and even then the qualitative features are reasonable, but some details are not reproduced well) involves the processes when the solitons come very close together (within one width of each other) during their scattering.