A general approach for getting the commutator representations of the hierarchies of nonlinear evolution equations

Abstract A general approach for generating the commutator representations of the hierarchies of nonlinear evolution equations (NLEEs) is presented. For this approach, three concrete examples are given.

[1]  Tu Guizhang,et al.  The trace identity, a powerful tool for constructing the hamiltonian structure of integrable systems (II) , 1989 .

[2]  Gui‐zhang Tu,et al.  The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems , 1989 .

[3]  H. Flaschka On the Toda Lattice. II Inverse-Scattering Solution , 1974 .

[4]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[5]  Xianguo Geng,et al.  A nonconfocal generator of involutive systems and three associated soliton hierarchies , 1991 .

[6]  Marcel Jaulent,et al.  Nonlinear evolution equations associated with ‘enegry-dependent Schrödinger potentials’ , 1976 .

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

[8]  G. Bluman,et al.  On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)]−(∂u/∂t)=0 , 1980 .

[9]  Athanassios S. Fokas,et al.  A symmetry approach to exactly solvable evolution equations , 1980 .

[10]  Four new hierarchies of nonlinear evolution equations , 1990 .

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

[12]  Masaaki Ito,et al.  Symmetries and conservation laws of a coupled nonlinear wave equation , 1982 .

[13]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[14]  James G. Berryman,et al.  Nonlinear Diffusion Problem Arising in Plasma Physics , 1978 .

[15]  G. Tu Liouville Integrability of Zero Curvature Equations , 1990 .

[16]  S. U. Campisano,et al.  A melting model for pulsing‐laser annealing of implanted semiconductors , 1979 .

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

[18]  R. L. Anderson,et al.  On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems , 1982 .