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

Expanding the scope of alkyne-mediated bioconjugations utilizing unnatural amino acids

The importance of bioconjugates within the field of chemistry drives the need for novelmethodologies for their preparation. Well-defined and stable bioconjugates are easily accessible via the utilization of unnatural amino acids (UAAs). As such, we have synthesized and incorporated two new UAAs into green fluorescent protein, and optimized a novel Cadiot-Chodkiewicz bioconjugation, effectively expanding the toolbox of chemical reactions that can be employed in the preparation of bioconjugates

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

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

The influence of severe wildfire on a threatened arboreal mammal

ContextFire regimes are changing with ongoing climate change, which is leading to an increase in fire frequency and severity. Australia’s Black Summer wildfires burned >12 million hectares in 2019–2020, affecting numerous threatened animal species. One of the species predicted to be most impacted was the threatened southern greater glider, an arboreal, hollow-dependent folivore, endemic to eastern Australia’s eucalypt forests.AimsThis study aimed to assess how the 2019–2020 wildfires affected greater glider abundance and the resources they depend on in Woomargama National Park, New South Wales, Australia.MethodsWe categorised 32 sites into four fire severity treatments with eight sites for each treatment: unburned (continuous unburned vegetation); refuges (unburned patches within the fire’s perimeter); low-moderate severity; and high severity. We carried out two spotlight surveys per site using the double-observer method, beginning 21 months after the fires. We also conducted vegetation assessments on the same transects. To analyse the data, we used Generalised Linear Models to compare habitat differences based on fire severity, and N-mixture models to model greater glider detectability and abundance in relation to habitat and fire severity.Key resultsWe found that fire severity depleted several habitat variables including canopy cover and the number of potentially hollow-bearing trees, a resource that greater gliders rely on. Greater glider abundance also decreased in all burn categories, with the greatest decline experienced in areas burned at high severity. We also found that greater glider abundance was much lower in fire refuges than unburned habitat outside of the fire zone.ConclusionsGreater glider declines following severe wildfire can be at least partly attributed to the level of vegetation loss and the associated loss of key habitat resources. The contribution of direct mortality to population declines remains unknown.ImplicationsGreater glider conservation will rely heavily on protecting expansive unburned areas of suitable habitat and maintaining hollow-bearing trees