scholarly journals Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations

1999 ◽  
Vol 40 (5) ◽  
pp. 2400-2418 ◽  
Author(s):  
Wen-Xiu Ma ◽  
Benno Fuchssteiner
Keyword(s):  
Algebraic Structure ◽  
Evolution Equations ◽  
Zero Curvature ◽  
Discrete Evolution Equations

EQUATION-FREE, EFFECTIVE COMPUTATION FOR DISCRETE SYSTEMS: A TIME STEPPER BASED APPROACH

2005 ◽  
Vol 15 (03) ◽  
pp. 975-996 ◽  
Author(s):  
J. MÖLLER ◽  
O. RUNBORG ◽  
P. G. KEVREKIDIS ◽  
K. LUST ◽  
I. G. KEVREKIDIS
Keyword(s):  
Evolution Equations ◽  
Time Integration ◽  
Discrete Systems ◽  
Computer Assisted ◽  
Discrete Problem ◽  
Arc Length ◽  
Effective Equation ◽  
Discrete Evolution Equations ◽  
Coarse Model ◽  
The Continuum

We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be explicitly constructed. The method only uses a time-integration code for the discrete problem and judicious choices of initial data and integration times; our bifurcation computations are based on the so-called Recursive Projection Method (RPM) with arc-length continuation [Shroff & Keller, 1993]. The technique is used to monitor features of the genuinely discrete problem such as the pinning of coherent structures and its results are compared to quasi-continuum approaches such as the ones based on Padé approximations.

AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS

2011 ◽  
Vol 25 (23n24) ◽  
pp. 3237-3252 ◽  
Author(s):  
LIN LUO ◽  
WEN-XIU MA ◽  
ENGUI FAN
Keyword(s):  
Lie Algebras ◽  
Algebraic Structure ◽  
Algebraic Structures ◽  
Direct Sums ◽  
Zero Curvature ◽  
Integrable Couplings ◽  
Symmetry Algebras

We establish an algebraic structure for zero curvature representations of coupled integrable couplings. The adopted zero curvature representations are associated with Lie algebras possessing two sub-Lie algebras in form of semi-direct sums of Lie algebras. By applying the presented algebraic structures to the AKNS systems, we give an approach for generating τ-symmetry algebras of coupled integrable couplings.

TWO SUPER-INTEGRABLE SYSTEMS AND ASSOCIATED SUPER-HAMILTONIAN STRUCTURES

2009 ◽  
Vol 23 (27) ◽  
pp. 3253-3264 ◽  
Author(s):  
QIU-LAN ZHAO ◽  
XIN-YUE LI ◽  
BAI-YING HE
Keyword(s):  
Integrable Systems ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Lie Superalgebras ◽  
Nonlinear Evolution Equations ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Zero Curvature

The super extensions of g-cKdV and mKdV integrable systems are proposed. Two hierarchies of super-integrable nonlinear evolution equations are found. In addition, making use of the super-trace identity, we construct the super-Hamiltonian structures of zero-curvature equations associated with Lie superalgebras.

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