Erratum on “Some Symmetry Classifications of Hyperbolic Vector Evolution Equations”:J Nonlinear Math. Phys.12suppl. 1 (2005), 13–31

2005 ◽  
Vol 12 (4) ◽  
pp. 607-608 ◽  
Author(s):  
Stephen C Anco ◽  
Thomas Wolf
Keyword(s):  
Evolution Equations ◽  
Nonlinear Math ◽  
Math Phys

scholarly journals CLASSIFICATION OF GRADED LEFT-SYMMETRIC ALGEBRAIC STRUCTURES ON WITT AND VIRASORO ALGEBRAS

2011 ◽  
Vol 22 (02) ◽  
pp. 201-222 ◽  
Author(s):  
XIAOLI KONG ◽  
HONGJIA CHEN ◽  
CHENGMING BAI
Keyword(s):  
Virasoro Algebra ◽  
Indecomposable Module ◽  
Multiplication Operators ◽  
Algebraic Structures ◽  
Witt Algebra ◽  
Left Multiplication ◽  
Symmetric Algebras ◽  
Nonlinear Math ◽  
Math Phys

We find that a compatible graded left-symmetric algebraic structure on the Witt algebra induces an indecomposable module V of the Witt algebra with one-dimensional weight spaces by its left-multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebraic structures on the Witt algebra are classified. All of them are simple and they include the examples given by [Comm. Algebra32 (2004) 243–251; J. Nonlinear Math. Phys.6 (1999) 222–245]. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebraic structures on the Virasoro algebra. They coincide with the examples given by [J. Nonlinear Math. Phys.6 (1999) 222–245].

scholarly journals METRIC COMPATIBLE OR NON-COMPATIBLE FINSLER–RICCI FLOWS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250041 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Ricci Flow ◽  
Evolution Equations ◽  
Finsler Geometry ◽  
Flow Theory ◽  
Finsler Metric ◽  
Geometric Evolution ◽  
Ricci Flows ◽  
Canonical Metric ◽  
Self Consistent ◽  
Math Phys

There were elaborated different models of Finsler geometry using the Cartan (metric compatible), or Berwald and Chern (metric non-compatible) connections, the Ricci flag curvature, etc. In a series of works, we studied (non)-commutative metric compatible Finsler and non-holonomic generalizations of the Ricci flow theory [see S. Vacaru, J. Math. Phys. 49 (2008) 043504; 50 (2009) 073503 and references therein]. The aim of this work is to prove that there are some models of Finsler gravity and geometric evolution theories with generalized Perelman's functionals, and correspondingly derived non-holonomic Hamilton evolution equations, when metric non-compatible Finsler connections are involved. Following such an approach, we have to consider distortion tensors, uniquely defined by the Finsler metric, from the Cartan and/or the canonical metric compatible connections. We conclude that, in general, it is not possible to elaborate self-consistent models of geometric evolution with arbitrary Finsler metric non-compatible connections.

SCHRÖDINGER–LICHNEROWICZ LIKE FORMULA ON KÄHLER–NORDEN MANIFOLDS

2012 ◽  
Vol 09 (01) ◽  
pp. 1250010 ◽  
Author(s):  
NEDİM DEĞİRMENCI ◽  
ŞENAY KARAPAZAR
Keyword(s):  
Dirac Operator ◽  
Nonlinear Math ◽  
Math Phys

A new kind of spinors and Dirac operator are introduced on Kähler–Norden manifolds in [Spinors on Kähler–Norden manifolds, J. Nonlinear Math. Phys.17(1) (2010) 27–34]. In this work the square D2 of the Dirac operator D is computed and a kind of Schrödinger–Lichnerowicz formula is obtained.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

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