Reduced D-Kaup–Newell soliton hierarchies from sl(2,ℝ) and so(3,ℝ)

Two reduced D-Kaup–Newell spectral problems from sl(2,ℝ) and so(3,ℝ) are considered, and the corresponding soliton hierarchies are generated by using the zero curvature formulation. The resulting systems are shown to be bi-Hamiltonian and their hereditary recursion operators are explicitly computed.

[1]  M. Boiti,et al.  Canonical structure of soliton equations via isospectral eigenvalue problems , 1984 .

[2]  Wen-Xiu Ma,et al.  Integrable couplings and matrix loop algebras , 2013 .

[3]  Athanassios S. Fokas,et al.  Symplectic structures, their B?acklund transformation and hereditary symmetries , 1981 .

[4]  Variational identities and Hamiltonian structures , 2010 .

[5]  Wen-Xiu Ma.  A soliton hierarchy associated with so(3, R)so(3, R) , 2013, Appl. Math. Comput..

[6]  Wen-Xiu Ma,et al.  Integrable counterparts of the D-Kaup-Newell soliton hierarchy , 2014, Appl. Math. Comput..

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

[8]  L. Urrutia,et al.  最大エネルギーレベルを有するSU(2).×.SU(2)ジェインズ-カミングス(Jaynes-Cummings)モデル , 2014 .

[9]  B. Fuchssteiner,et al.  Integrable theory of the perturbation equations , 1996, solv-int/9604004.

[10]  Benno Fuchssteiner,et al.  Application of hereditary symmetries to nonlinear evolution equations , 1979 .

[11]  A Counterpart of the Wadati–Konno–Ichikawa Soliton Hierarchy Associated with so(3,R) , 2014, 1405.1089.

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

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

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

[15]  T. Koikawa,et al.  Canonical structure of soliton equations. I , 1982 .

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

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

[18]  Jingsong He,et al.  A supertrace identity and its applications to superintegrable systems , 2008 .

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

[20]  Wenxiu Ma,et al.  A generalized Kaup-Newell spectral problem, soliton equations and finite-dimensional integrable systems , 1995 .

[21]  Zixiang Zhou,et al.  Coupled Integrable Systems Associated with a Polynomial Spectral Problem and Their Virasoro Symmetry Algebras , 1996, solv-int/9607003.

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

[23]  Franco Magri,et al.  A Simple model of the integrable Hamiltonian equation , 1978 .

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

[25]  Engui Fan,et al.  Integrable evolution systems based on Gerdjikov-Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation , 2000 .

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

[27]  P. Kulish,et al.  Quadratic bundle and nonlinear equations , 1980 .

[28]  A 3 sx 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization , 1995, solv-int/9510012.