This is the first part of a study, consisting of two parts, on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, using linear combinations of Lax matrices of soliton hierarchies, we introduce trigonal curves by their characteristic equations, explore general properties of meromorphic functions defined as ratios of the Baker-Akhiezer functions, and determine zeros and poles of the Baker-Akhiezer functions and their Dubrovin-type equations. We analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5549571 | PMC |
| http://dx.doi.org/10.1098/rspa.2017.0232 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Roses in the nonperturbative current response of artificial crystals.
Proc Natl Acad Sci U S A
October 2023
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104.
In two-dimensional artificial crystals with large real-space periodicity, the nonlinear current response to a large applied electric field can feature a strong angular dependence, which encodes information about the band dispersion and Berry curvature of isolated electronic Bloch minibands. Within the relaxation-time approximation, we obtain analytic expressions up to infinite order in the driving field for the current in a band-projected theory with time-reversal and trigonal symmetry. For a fixed field strength, the dependence of the current on the direction of the applied field is given by rose curves whose petal structure is symmetry constrained and is obtained from an expansion in real-space translation vectors.
View Article and Find Full Text PDFHafnium(IV) Chemistry with Imide-Dioxime and Catecholate-Oxime Ligands: Unique {Hf} and Metalloaromatic {Hf}-Oxo Clusters Exhibiting Fluorescence.
Inorg Chem
December 2022
Section of Inorganic and Analytical Chemistry, University of Ioannina, Ioannina45110, Greece.
Hafnium(IV) molecular species have gained increasing attention due to their numerous applications ranging from high-resolution nanolithography, heterogeneous catalysis, and electronics to the design of molecule-based building blocks in metal-organic frameworks (MOFs), with applications in gas separation, sorption, luminescence sensing, and interim storage of radioactive waste. Despite great potential, their chemistry is relatively underdeveloped. Here, we use strong chelators (2-6)-piperidine-2,6-dione (Hpidiox) and 2,3-dihydroxybenzaldehyde oxime (Hdihybo) to synthesize the first ever reported pentanuclear {Hf/Hpidiox} and hexanuclear {Hf/Hdihybo} clusters (HfOCs).
View Article and Find Full Text PDFStructure and Magnetism of an Ideal One-Dimensional Chain Antiferromagnet [CNH][Fe(SO)] with a Large Spin of = 5/2.
Inorg Chem
September 2022
Wuhan National High Magnetic Field Center & School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.
Isolated large-spin Heisenberg antiferromagnetic uniform chain is quite rare. Here, we have successfully synthesized an ideal one-dimensional (1D) = 5/2 linear-chain antiferromagnet [CNH][Fe(SO)], which crystallizes in a trigonal lattice with the space group 3. A broad maximum at = 18 K is observed in the magnetic susceptibility curve.
View Article and Find Full Text PDFEnhancing the Luminescence of Eu(III) Complexes with the Ruthenocene Organometallic Unit as Ancillary Ligand.
Inorg Chem
August 2022
Department of Chemistry, Federal University of Paraíba, 58051-970 João Pessoa, Paraiba, Brazil.
Five novel Eu(III)-β-diketonate complexes containing ruthenocene ancillary ligands (1,1'-bis(diphenylphosphoryl)ruthenocene─RcBPO) were synthesized and characterized. The coordination compounds presented the general formula [Eu(β-dik)(RcBPO)], where β-dik stands for 2-thenoyltrifluoroacetonate (tta), 3-benzoyl-1,1,1-trifluoroacetone (btf), 2-dibenzoylmethanate (dbm), 2-acetyl-1,3-indandionate (aind), and 2-benzoyl-1,3-indandionate (bind), and RcBPO stands for 1,1'-bis(diphenylphosphoryl)ruthenocene. The [Eu(aind)(RcBPO)] complex crystallizes in a monoclinic Cc non-centrosymmetric space group with the europium site environment, assuming a bicapped trigonal prism coordination polyhedron with the symmetry point group close to .
View Article and Find Full Text PDFModulating aryl substitution: Does it play a role in the anti-leishmanial activity of a series of tetra-aryl Sb(V) fluorinated carboxylates?
J Inorg Biochem
September 2022
Department of Chemistry, Institute of Natural Sciences, South Ural State University, 76 Lenin prospekt, Chelyabinsk 454080, Russian Federation.
Eight tetra-arylantimony carboxylates of the general formula ArSbOC(O)R with Ar = Ph (a), p-Tol (b), R = CF (1), CHCF (2), CFBr (3), CFCFCF (4) have been synthesised and characterised. Two of them (2b, 3b) are structurally novel. All structures were analytically characterised by FT-IR, H, C NMR spectroscopy.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!