Classification and Recursion Operators of Dark Burgers’ Equation

2018 ◽  
Vol 73 (2) ◽  
pp. 175-180 ◽  
Author(s):  
Mei-Dan Chen ◽  
Biao Li
Keyword(s):  
Symbolic Computation ◽  
Free Parameter ◽  
Burgers Equation ◽  
Differential Polynomial ◽  
Higher Order ◽  
Recursion Operators ◽  
Burgers Equations ◽  
Dual Symmetry ◽  
Free Parameters

AbstractWith the help of symbolic computation, two types of complete scalar classification for dark Burgers’ equations are derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark Burgers’ systems; so some special equations including symmetry equation and dual symmetry equation are obtained by selecting the free parameter. Furthermore, two kinds of recursion operators for these dark Burgers’ equations are constructed by two direct assumption methods.

HIGHER ORDER BURGERS EQUATION

1986 ◽  
Vol 6 (3) ◽  
pp. 353-360 ◽  
Author(s):  
Mingliang Wang
Keyword(s):  
Burgers Equation ◽  
Higher Order

scholarly journals Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 57
Author(s):  
Max-Olivier Hongler
Keyword(s):  
Burgers Equation ◽  
Higher Order ◽  
Underlying Structure ◽  
Swarm Dynamics ◽  
Special Cases ◽  
Kink Waves ◽  
Systematic Derivation ◽  
Fifth Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

scholarly journals Clustering Single-Cell RNA-Seq Data with Regularized Gaussian Graphical Model

Genes ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 311
Author(s):  
Zhenqiu Liu
Keyword(s):  
Single Cell ◽  
Free Parameter ◽  
Graphical Model ◽  
Expression Patterns ◽  
Information Criterion ◽  
Log P ◽  
Rna Seq ◽  
Clustering Methods ◽  
Wide Range ◽  
Free Parameters

Single-cell RNA-seq (scRNA-seq) is a powerful tool to measure the expression patterns of individual cells and discover heterogeneity and functional diversity among cell populations. Due to variability, it is challenging to analyze such data efficiently. Many clustering methods have been developed using at least one free parameter. Different choices for free parameters may lead to substantially different visualizations and clusters. Tuning free parameters is also time consuming. Thus there is need for a simple, robust, and efficient clustering method. In this paper, we propose a new regularized Gaussian graphical clustering (RGGC) method for scRNA-seq data. RGGC is based on high-order (partial) correlations and subspace learning, and is robust over a wide-range of a regularized parameter λ. Therefore, we can simply set λ=2 or λ=log(p) for AIC (Akaike information criterion) or BIC (Bayesian information criterion) without cross-validation. Cell subpopulations are discovered by the Louvain community detection algorithm that determines the number of clusters automatically. There is no free parameter to be tuned with RGGC. When evaluated with simulated and benchmark scRNA-seq data sets against widely used methods, RGGC is computationally efficient and one of the top performers. It can detect inter-sample cell heterogeneity, when applied to glioblastoma scRNA-seq data.

scholarly journals Recursion operators admitted by non-Abelian Burgers equations: Some remarks

2018 ◽  
Vol 147 ◽  
pp. 40-51 ◽  
Author(s):  
Sandra Carillo ◽  
Mauro Lo Schiavo ◽  
Cornelia Schiebold
Keyword(s):  
Recursion Operators ◽  
Burgers Equations

Generalized Burgers Equations Transformable to the Burgers Equation

2011 ◽  
Vol 127 (3) ◽  
pp. 211-220 ◽  
Author(s):  
B. Mayil Vaganan ◽  
T. Jeyalakshmi
Keyword(s):  
Burgers Equation ◽  
Burgers Equations

Soliton solutions of Burgers equations and perturbed Burgers equation

2010 ◽  
Vol 216 (11) ◽  
pp. 3370-3377 ◽  
Author(s):  
Anwar Ja’afar Mohamad Jawad ◽  
Marko D. Petković ◽  
Anjan Biswas
Keyword(s):  
Burgers Equation ◽  
Soliton Solutions ◽  
Burgers Equations

Higher Order Solution of Nonlinear Waves. II. Shock Wave Described by Burgers Equation

1997 ◽  
Vol 66 (4) ◽  
pp. 984-987 ◽  
Author(s):  
Shinsuke Watanabe ◽  
Shingo Ishiwata ◽  
Katsuyuki Kawamura ◽  
Heung Geun Oh
Keyword(s):  
Shock Wave ◽  
Nonlinear Waves ◽  
Burgers Equation ◽  
Higher Order ◽  
Order Solution

scholarly journals Anti-periodic traveling wave solutions to a class of higher-order Kadomtsev-Petviashvili-Burgers equations

1994 ◽  
Vol 7 (1) ◽  
pp. 1-12
Author(s):  
Sergiu Aizicovici ◽  
Yun Gao ◽  
Shih-Liang Wen
Keyword(s):  
Traveling Wave ◽  
Continuous Dependence ◽  
Traveling Wave Solutions ◽  
Higher Order ◽  
Two Dimensional ◽  
Burgers Equations ◽  
Wave Solutions ◽  
Periodic Traveling Wave ◽  
Continuous Dependence On Data

We discuss the existence, uniqueness, and continuous dependence on data, of anti-periodic traveling wave solutions to higher order two-dimensional equations of Korteweg-deVries type.

scholarly journals Exact statistical properties of the Burgers equation

2000 ◽  
Vol 417 ◽  
pp. 323-349 ◽  
Author(s):  
L. FRACHEBOURG ◽  
Ph. A. MARTIN
Keyword(s):  
White Noise ◽  
Large Distance ◽  
Burgers Equation ◽  
Higher Order ◽  
Statistical Properties ◽  
Inviscid Limit ◽  
Initial Condition ◽  
Spatial Correlations ◽  
One Dimensional ◽  
The One

The one-dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed analytical forms. In particular, the large distance behaviour of spatial correlations of the field is determined. Since higher-order distributions factorize in terms of the one- and two- point functions, our analysis provides an explicit and complete statistical description of this problem.

scholarly journals KAON WEAK DECAYS IN CHIRAL THEORIES

1999 ◽  
Vol 14 (19) ◽  
pp. 1273-1285 ◽  
Author(s):  
M. D. SCADRON
Keyword(s):  
Perturbation Theory ◽  
Free Parameter ◽  
Sigma Model ◽  
Axial Current ◽  
Linear Sigma Model ◽  
Pole Model ◽  
Chiral Perturbation ◽  
Weak Decays ◽  
Partial Conservation ◽  
Free Parameters

The ten nonleptonic weak decays K→2π, K→ 3π, KL→2γ, KS→2γ, KL→π02γ, are predicted for a chiral pole model based on the linear sigma model theory which automatically satisfies the partial conservation of axial current (PCAC) hypothesis. These predictions, agreeing with data to the 5% level and containing no or at most one free parameter, are compared with the results of chiral perturbation theory (ChPT). The latter ChPT approach to one-loop level is known to contain at least four free parameters and then predicts a KL→π0γγ rate which is 60% shy of the experimental value.

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