Matrix Spectral Problems and Integrability Aspects of the Błaszak-Marciniak Lattice Equations
Sign Up to like & getrecommendations! Published in 2020 at "Reports on Mathematical Physics"
DOI: 10.1016/s0034-4877(20)30087-2
Abstract: A method to derive the matrix spectral problems of the Blaszak–Marciniak lattice equations is proposed, and the matrix Lax representations of all the three-field and four-field Blaszak-Marciniak lattice equations are given explicitly. The integrability aspects… read more here.
Keywords: integrability aspects; spectral problems; marciniak lattice; lattice equations ... See more keywords
Determination of scale invariance in random-matrix spectral fluctuations without unfolding.
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DOI: 10.1103/physreve.96.012110
Abstract: We apply the singular value decomposition (SVD) method, based on normal-mode analysis, to decompose the spectra of finite random matrices of standard Gaussian ensembles in trend and fluctuation modes. We use the fact that the… read more here.
Keywords: determination scale; scale invariance; random matrix; invariance random ... See more keywords
Crossover in nonstandard random-matrix spectral fluctuations without unfolding.
Sign Up to like & getrecommendations! Published in 2018 at "Physical Review E"
DOI: 10.1103/physreve.98.022110
Abstract: Recently, singular value decomposition (SVD) was applied to standard Gaussian ensembles of random-matrix theory to determine the scale invariance in spectral fluctuations without performing any unfolding procedure. Here, SVD is applied directly to the β-Hermite… read more here.
Keywords: spectral fluctuations; crossover nonstandard; nonstandard random; random matrix ... See more keywords
Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies
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DOI: 10.3390/math11081794
Abstract: Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their… read more here.
Keywords: hamiltonian hierarchies; matrix spectral; higher order; integrable hamiltonian ... See more keywords