A generalized Dirac soliton hierarchy and its bi-Hamiltonian structure

Abstract By using symbolic computation software(Maple), a generalized Dirac soliton hierarchy is derived from a new matrix spectral problem associated with the Lie algebra sl ( 2 , R ) . A bi-Hamiltonian structure yielding Liouville integrability is furnished by the trace identity.

[1]  Chaudry Masood Khalique,et al.  A direct bilinear Bäcklund transformation of a (2+1)-dimensional Korteweg-de Vries-like model , 2015, Appl. Math. Lett..

[2]  H. Grosse.  New solitons connected to the Dirac equation , 1986 .

[3]  Wen-Xiu Ma,et al.  A coupled AKNS–Kaup–Newell soliton hierarchy , 1999 .

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

[5]  Xi-Xiang Xu,et al.  A generalized Wadati–Konno–Ichikawa hierarchy and new finite-dimensional integrable systems , 2002 .

[6]  Allan P. Fordy,et al.  Coupled Harry Dym equations with multi-Hamiltonian structures , 1988 .

[7]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[8]  Yufeng Zhang,et al.  The quadratic-form identity for constructing the Hamiltonian structure of integrable systems , 2005 .

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

[10]  A. Fordy,et al.  Coupled KdV equations with multi-Hamiltonian structures , 1987 .

[11]  Chaudry Masood Khalique,et al.  Envelope bright- and dark-soliton solutions for the Gerdjikov–Ivanov model , 2015 .

[12]  M. Boiti,et al.  The Nonlinear Evolution Equations Related to the Wadati-Konno-Ichikawa Spectral Problem , 1983 .

[13]  A. Fokas,et al.  The hierarchy of the Benjamin-Ono equation , 1981 .

[14]  A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order , 2007 .

[15]  Xing Lü,et al.  Madelung fluid description on a generalized mixed nonlinear Schrödinger equation , 2015 .

[16]  Tu Gui-Zhang,et al.  On Liouville integrability of zero-curvature equations and the Yang hierarchy , 1989 .

[17]  Fuhong Lin,et al.  Analytical study on a two-dimensional Korteweg–de Vries model with bilinear representation, Bäcklund transformation and soliton solutions , 2015 .

[18]  Chaudry Masood Khalique,et al.  Solitary waves with the Madelung fluid description: A generalized derivative nonlinear Schrödinger equation , 2016, Commun. Nonlinear Sci. Numer. Simul..

[19]  Inverse scattering on the line for a Dirac system , 1991 .

[20]  Shoufeng Shen,et al.  New Soliton Hierarchies Associated with the Lie Algebra so(3,ℝ) and their BI-Hamiltonian Structures , 2015 .

[21]  Kimiaki Konno,et al.  New Integrable Nonlinear Evolution Equations , 1979 .

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

[23]  Andrew G. Glen,et al.  APPL , 2001 .

[24]  An so (3, ℝ) Counterpart of the Dirac Soliton Hierarchy and its Bi-Integrable Couplings , 2014 .

[25]  Xing Lü,et al.  Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order , 2016, Commun. Nonlinear Sci. Numer. Simul..

[26]  David J. Kaup,et al.  An exact solution for a derivative nonlinear Schrödinger equation , 1978 .

[27]  An integrable counterpart of the D-AKNS soliton hierarchy from so(3,R) , 2014 .

[28]  M. Ablowitz,et al.  The Inverse scattering transform fourier analysis for nonlinear problems , 1974 .