On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits

In this paper, we construct grammian-like quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Through continuum limits of this non-Abelian Hirota-Miwa equation and its quasideterminant solutions, we construct a cascade of noncommutative differential-difference equations ending with the noncommutative KP equation. For each of these systems the quasideterminant solutions are constructed as well.Comment: 9 pages, 1 figur

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.Comment: 2 figure

On pattern structures of the N-soliton solution of the discrete KP equation over a finite field

The existence and properties of coherent pattern in the multisoliton solutions of the dKP equation over a finite field is investigated. To that end, starting with an algebro-geometric construction over a finite field, we derive a "travelling wave" formula for $N$-soliton solutions in a finite field. However, despite it having a form similar to its analogue in the complex field case, the finite field solutions produce patterns essentially different from those of classical interacting solitons.Comment: 12 pages, 3 figure

Experimental investigation of NO reburning during oxy-coal burner staging

This study presents an investigation into the impact of varied burner staging environments on an oxy-fuel flame and the rate of the NO formation and destruction processes. The experimental data was extracted from the use of a 250 kWth down-fired combustion test facility with a scaled-down model of an industrial low-NOx burner (LNB). Two oxy-coal combustion regimes were investigated by varying a fixed flow of oxidant between the secondary and tertiary registers, so as to impact the stoichiometry in the fuel-rich region and flame structure, and using various NO recycling regimes, to test the impact of these different burner configurations on NO reburning. The data was collected by monitoring key emissions in the flue gas and in the flame, as well as temperatures throughout the furnace and the unburned carbon content of the ash. A detailed investigation encompassing the impact of secondary oxidant proportion for different oxidants on NO emissions, together with the quantification of recycled NO destruction, is discussed. This investigation finds that 85 % to 95 % of the recycled NO is destroyed at a range of burner configurations using OF 27 and OF 30 at 170 kWth. In addition to this, NO formation and carbon burnout are found to be significantly affected with changing burner configurations. Further to this, OF 30 flames appear to be more sensitive to burner configuration than OF 27 flames with regards to both NO formation and destruction, possibly due to the decreased density of the OF 30 oxidant. Radial profiles of two burner configurations at OF 27 and OF 30, as well as an axial profile of two burner configurations at OF 30, are analysed. The profiles appear to show that burner staging aids in controlling the products of NO reburning, hence maximising the destruction of recycled NO

Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters

We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the 6N-dimensional phase space Omega of the relativistic systems with 2N particles and N antiparticles, there exists a 2N-dimensional Poincaré-invariant submanifold OmegaP corresponding to N free particles and N bound particle-antiparticle pairs in their ground state. The Tzitzeica N-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of OmegaP. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state