An integrable couplings of Dirac soliton hierarchy with self-consistent sources

Abstract A kind of the integrable couplings of soliton equations hierarchy with self-consistent sources associated with sl ˜ ( 4 ) is presented. As an application example, we construct a new integrable couplings of the Dirac soliton hierarchy with self-consistent sources by using of loop algebra sl ˜ ( 4 ) .

[1]  Yufeng Zhang,et al.  A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling , 2003 .

[2]  The general scheme for higher-order decompositions of zero-curvature equations associated with 337-1337-1337-1(2) , 1996 .

[3]  Wen-Xiu Ma,et al.  A discrete variational identity on semi-direct sums of Lie algebras , 2007, 0711.1147.

[4]  Peter D. Lax,et al.  Periodic solutions of the KdV equation , 2010 .

[5]  Wen-Xiu Ma,et al.  Semi-direct sums of Lie algebras and continuous integrable couplings , 2006, nlin/0603064.

[6]  Wen-Xiu Ma,et al.  Soliton, Positon and Negaton Solutions to a Schrödinger Self-consistent Source Equation , 2003 .

[7]  The multi-component generalized Wadati-Konono-Ichikawa (WKI) hierarchy and its multi-component integrable couplings system with two arbitrary functions , 2005 .

[8]  Wen-Xiu Ma,et al.  Complexiton solutions of the Korteweg-de Vries equation with self-consistent sources , 2005 .

[9]  Wen-Xiu Ma,et al.  Enlarging spectral problems to construct integrable couplings of soliton equations , 2003 .

[10]  Fan En-gui,et al.  Characteristic Numbers of Matrix Lie Algebras , 2008 .

[11]  Wen-Xiu Ma,et al.  Semidirect sums of Lie algebras and discrete integrable couplings , 2006 .

[12]  V. K. Mel’nikov.  Wave emission and absorption in a nonlinear integrable system , 1986 .

[13]  W. Ma,et al.  Virasoro symmetry algebra of Dirac soliton hierarchy , 1996, solv-int/9609006.

[14]  MA W.X.,et al.  Integrable Theory of the Perturbation Equations , 2004 .

[15]  Yi Zhang,et al.  The multi-component coupled Burgers hierarchy of soliton equations and its multi-component integrable couplings system with two arbitrary functions , 2004 .

[16]  Wenxiu Ma,et al.  Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras , 2006 .

[17]  Peter A. Clarkson,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering: Remarks on Riemann-Hilbert problems , 1991 .

[18]  Wen-Xiu Ma,et al.  THE BI-HAMILTONIAN STRUCTURE OF THE PERTURBATION EQUATIONS OF THE KDV HIERARCHY , 1996 .

[19]  V. K. Mel'nikov,et al.  Integration method of the Korteweg-de Vries equation with a self-consistent source , 1988 .

[20]  Wen-Xiu Ma,et al.  Integration of the soliton hierarchy with self-consistent sources , 2000 .

[21]  V. K. Mel’nikov.  Exact solutions of the Korteweg-de Vries equation with a self-consistent source , 1988 .

[22]  Dengyuan Chen,et al.  The multi-component Yang hierarchy and its multi-component integrable coupling system with two arbitrary functions , 2005 .

[23]  Norman J. Zabusky,et al.  Soliton , 2010, Scholarpedia.

[24]  Wen-Xiu Ma.  Integrable couplings of vector AKNS soliton equations , 2005 .

[25]  THE GENERAL SCHEME FOR HIGHER-ORDER DECOMPOSITIONS OF ZERO-CURVATURE EQUATIONS ASSOCIATED WITH s/(2) , 1996 .

[26]  Hong-qing Zhang,et al.  A new loop algebra system and its discrete integrable coupling system , 2007 .