A hierarchy of nonlinear evolution equations, its bi-Hamiltonian structure, and finite-dimensional integrable systems

2000 ◽  
Vol 41 (4) ◽  
pp. 2058-2065 ◽  
Author(s):  
Fan Engui ◽  
Zhang Hongqing
Keyword(s):  
Integrable Systems ◽  
Hamiltonian Structure ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Finite Dimensional

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.

A LIE SUPERALGEBRA AND CORRESPONDING HIERARCHY OF EVOLUTION EQUATIONS

2009 ◽  
Vol 23 (28) ◽  
pp. 3387-3396 ◽  
Author(s):  
XIN-ZENG WANG ◽  
HUAN-HE DONG
Keyword(s):  
Hamiltonian Structure ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Lie Superalgebra ◽  
Nonlinear Evolution Equations ◽  
Isospectral Problem

A Lie super algebra G is constructed and an isospectral problem with five potentials is designed. From there, a corresponding hierarchy of nonlinear evolution equations is derived and super-AKNS, super-TD, super-D-AKNS are deduced. Their super-Hamiltonian structure is established by making use of the supertrace identity, and they are intergrable in sense of Liouville.

Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities

1995 ◽  
Vol 125 (2) ◽  
pp. 225-246 ◽  
Author(s):  
Victor A. Galaktionov
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Invariant Subspaces ◽  
Nonlinear Evolution Equations ◽  
Heat Equations ◽  
Explicit Solutions ◽  
Finite Dimensional ◽  
Quadratic Nonlinearities ◽  
Image Position ◽  
Spatial Operators

We present new explicit solutions to some classes of quasilinear evolution equations arising in different applications, including equations of the Boussinesq type:and quasilinear heat equations:The method is based on construction of finite-dimensional linear functional subspaces which are invariant with respect to spatial operators having quadratic nonlinearities. The corresponding nonlinear evolution equations on invariant subspaces are shown to be equivalent to finite-dimensional dynamical systems. Examples of two-, three- and five- dimensional invariant subspaces are given. Some generalisations to N-dimensional quadratic operators are also considered.

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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