$W$-representations of two-matrix models with infinite set of variables

Wang, Lu-Yao; Zhu, Yusen; Chen, Ying; Bei, Kang

doi:10.48550/arxiv.2301.13696

Cited by 1 publication

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“…The degrees of operators are defined as deg(t [29]. Since the operators D and D − W being invertible and De N ( p j=1 t (j) 0 ) = 0, from (5), we have…”

Section: Complex Multi-matrix Model 21 W -Representation Of Complex M...mentioning

confidence: 99%

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History of Mathematics in American Mathematical Textbooks of the Late 19th and Early 20th Centuries

Wang

2021

School Mathematics Textbooks in China

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The logarithmic Schrödinger equation (LogSE) has a logarithmic nonlinearity f (u) = u ln |u| 2 that is not differentiable at u = 0. Compared with its counterpart with a regular nonlinear term, it possesses richer and unusual dynamics, though the low regularity of the nonlinearity brings about significant challenges in both analysis and computation. Among very limited numerical studies, the semi-implicit regularized method via regularising f (u) as u ε ln(ε+|u ε |) 2 to overcome the blowup of ln |u| 2 at u = 0 has been investigated recently in literature. With the understanding of f (0) = 0, we analyze the non-regularized first-order Implicit-Explicit (IMEX) scheme for the LogSE. We introduce some new tools for the error analysis that include the characterization of the Hölder continuity of the logarithmic term, and a nonlinear Grönwall's inequality. We provide ample numerical results to demonstrate the expected convergence. We position this work as the first one to study the direct linearized scheme for the LogSE as far as we can tell.

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“…The degrees of operators are defined as deg(t [29]. Since the operators D and D − W being invertible and De N ( p j=1 t (j) 0 ) = 0, from (5), we have…”

Section: Complex Multi-matrix Model 21 W -Representation Of Complex M...mentioning

confidence: 99%

“…It is useful to analyze the structures of matrix model, such as the spectral curve [15] and superintegrability [16]- [25]. The W -representations of two-matrix models have been studied [26]- [29]. The superintegrable multi-matrix model was constructed in Ref.…”

Section: Introductionmentioning

confidence: 99%

History of Mathematics in American Mathematical Textbooks of the Late 19th and Early 20th Centuries

Wang

2021

School Mathematics Textbooks in China

View full text Add to dashboard Cite

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$W$-representations of two-matrix models with infinite set of variables

Cited by 1 publication

References 20 publications

History of Mathematics in American Mathematical Textbooks of the Late 19th and Early 20th Centuries

History of Mathematics in American Mathematical Textbooks of the Late 19th and Early 20th Centuries

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