The Multi-Component Jaulent-Miodek Hierarchy and its Multi-Component Integrable Coupling System with Two Arbitrary Functions

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.442.124 ◽

2012 ◽

Vol 442 ◽

pp. 124-128

Author(s):

Jian Ya Ge ◽

Tie Cheng Xia

Keyword(s):

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

Loop Algebra ◽

Simple Loop ◽

Coupling System ◽

Integrable Couplings ◽

Isospectral Problem ◽

Integrable Coupling

We devise a new simple loop algebra GM and an isospectral problem. By making use of Tu scheme, the multi-component Jaulent-Miodek (JM) hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM the multi-component integrable couplings system with two arbitrary functions of the multi-component Jaulent-Miodek (JM) hierarchy are worked out. The method can be applied to other nonlinear evolution equations hierarchies.

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A New Approach for Generating the TX Hierarchy as well as Its Integrable Couplings

Abstract and Applied Analysis ◽

10.1155/2014/357621 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6

Author(s):

Guangming Wang

Keyword(s):

Hamiltonian Structure ◽

Evolution Equations ◽

Loop Algebra ◽

Integrable Hierarchy ◽

New Approach ◽

Zero Curvature ◽

Integrable Couplings ◽

Isospectral Problem ◽

Integrable Coupling

Tu Guizhang and Xu Baozhi once introduced an isospectral problem by a loop algebra with degree beingλ, for which an integrable hierarchy of evolution equations (called the TX hierarchy) was derived under the frame of zero curvature equations. In the paper, we present a loop algebra whose degrees are2λand2λ+1to simply represent the above isospectral matrix and easily derive the TX hierarchy. Specially, through enlarging the loop algebra with 3 dimensions to 6 dimensions, we generate a new integrable coupling of the TX hierarchy and its corresponding Hamiltonian structure.

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A LIE SUPERALGEBRA AND CORRESPONDING HIERARCHY OF EVOLUTION EQUATIONS

Modern Physics Letters B ◽

10.1142/s0217984909021429 ◽

2009 ◽

Vol 23 (28) ◽

pp. 3387-3396 ◽

Cited By ~ 4

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.

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(2+1)-DIMENSIONAL TD HIERARCHY AND ITS INTEGRABLE COUPLINGS

Modern Physics Letters B ◽

10.1142/s0217984907012815 ◽

2007 ◽

Vol 21 (07) ◽

pp. 407-413 ◽

Cited By ~ 5

Author(s):

ZHU LI ◽

HUAN-HE DONG

Keyword(s):

Loop Algebra ◽

Curvature Equation ◽

Zero Curvature ◽

Coupling System ◽

Integrable Couplings ◽

Integrable Coupling

Under the frame of the (2 + 1)-dimensional zero curvature equation and Tu model, the (2 + 1)-dimensional TD hierarchy is obtained. Again, by using the expanding loop algebra, the integrable coupling system of the above hierarchy is given.

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

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i3.470 ◽

2015 ◽

Vol 11 (3) ◽

pp. 3134-3138 ◽

Cited By ~ 3

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 andÂ reliability of the method are tested by its applications to the Couple Boiti-Leon-PempinelliÂ System which plays an important role in mathematical physics.

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