Soliton solutions of the Kadomtsev-Petviashvili II equation

We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form of its tau-function. We show that, in addition to previously known line-soliton solutions, this class also contains a large variety of new multi-soliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general, such solutions consist of unequal numbers of incoming and outgoing line solitons. From the asymptotic analysis of the tau-function, we explicitly characterize the incoming and outgoing line-solitons of this class of solutions. We illustrate these results by discussing several examples.Comment: 28 pages, 4 figure

On the equivalence of different approaches for generating multisoliton solutions of the KPII equation

The unexpectedly rich structure of the multisoliton solutions of the KPII equation has been explored by using different approaches, running from dressing method to twisting transformations and to the tau-function formulation. All these approaches proved to be useful in order to display different properties of these solutions and their related Jost solutions. The aim of this paper is to establish the explicit formulae relating all these approaches. In addition some hidden invariance properties of these multisoliton solutions are discussed

Grasslands as a Comparative for Farming Practices\u27 Influence on Carbon/Nitrogen Dynamics

A remnant prairie was used for comparison of the soil as a natural resource among alternative and conventional farming systems. Beginning and ending biotic and abiotic characteristics were quantified directly. Carbon and N flow was calculated using CENTURY model. Carbon decay was not tied to the size of the soil organic matter pool (SOM), but to crop choice. Nitrogen decay was linked to the size of the SOM pool. Nitrogen fertilizer depressed the amount of N mineralized by soil biota. The alternative farming systems in North Dakota (no-till and green-manure fallow) more nearly mimic the ecosystem processes of the prairie by increasing biotic storage (perennial roots and soil biota), increasing abiotic storage (residues), and slowing the flow of active soil C which helped slow and stabilize SOM-C

Retrospective short-term forecasting experiment in Italy based on the occurrence of strong (fore) shocks

In a recent work, we computed the relative frequencies with which strong shocks (4.0 ≤ Mw < 5.0), widely felt by the population were followed in the same area by po- tentially destructive main shocks (Mw ≥ 5.0) in Italy. Assuming the stationarity of the seismic release properties, such frequencies can be tentatively used to estimate the probabilities of potentially destructive shocks after the occurrence of future strong shocks. This allows us to set up an alarm-based forecasting hypothesis related to strong foreshocks occurrence. Such hypothesis is tested retrospectively on the data of a homogenized seismic catalogue of the Italian area against a purely random hypothesis that simply forecasts the target main shocks proportionally to the space–time fraction occupied by the alarms. We compute the latter frac- tion in two ways (i) as the ratio between the average time covered by the alarms in each area and the total duration of the forecasting experiment (60 yr) and (ii) as the same ratio but weighted by the past frequency of occurrence of earthquakes in each area. In both cases the overall retrospective performance of our forecasting algorithm is definitely better than the random case. Considering an alarm duration of three months, the algorithm retrospectively forecasts more than 70 per cent of all shocks with Mw ≥ 5.5 occurred in Italy from 1960 to 2019 with a total space–time fraction covered by the alarms of the order of 2 per cent. Considering the same space–time coverage, the algorithm is also able to retrospectively forecasts more than 40 per cent of the first main shocks with Mw ≥ 5.5 of the seismic sequences occurred in the same time interval. Given the good reliability of our results, the forecasting algorithm is set and ready to be tested also prospectively, in parallel to other ongoing procedures operating on the Italian territory

New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case

We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.Comment: Version to match the one which has been accepted for publication by J. Phys. A: Math. Theor. Added one figure, several comments and few references. (24 pages and 7 figures

Prospective randomized comparison of ultrasound-guided and neurostimulation techniques for continuous interscalene brachial plexus block in patients undergoing coracoacromial ligament repair

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Classification of the line-soliton solutions of KPII

In the previous papers (notably, Y. Kodama, J. Phys. A 37, 11169-11190 (2004), and G. Biondini and S. Chakravarty, J. Math. Phys. 47 033514 (2006)), we found a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation. The line-soliton solutions are solitary waves which decay exponentially in $(x,y)$-plane except along certain rays. In this paper, we show that those solutions are classified by asymptotic information of the solution as $|y| \to \infty$. Our study then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.Comment: 30 page