An isospectral problem with four potentials is discussed. The corresponding hierarchy of nonlinearevolution equations is derived. It is shown that the AKNS, Levi, D-AKNS hierarchies and a new oneare reductions of the ...An isospectral problem with four potentials is discussed. The corresponding hierarchy of nonlinearevolution equations is derived. It is shown that the AKNS, Levi, D-AKNS hierarchies and a new oneare reductions of the above hierarchy. In each case the relevant Hamiltonian form is established bymaking use of the trase identity.展开更多
On the basis of an analysis of the loop algebra ?_1 a new hierarchy of integrable sys-tems is proposed. The Hamiltonian structure of the new hierarchy of equations is established by means of constrained formal variati...On the basis of an analysis of the loop algebra ?_1 a new hierarchy of integrable sys-tems is proposed. The Hamiltonian structure of the new hierarchy of equations is established by means of constrained formal variational calculus. This hierarchy of evolution equations is demonstrated to possess an infinite number of conserved densities, which are ininvolution in pairs.展开更多
The background of the present investigation is the Darboux transformation (DT),which is nowadays an effective method in generating solutions of partial differential equations (PDE) (see [1—5] and the references there...The background of the present investigation is the Darboux transformation (DT),which is nowadays an effective method in generating solutions of partial differential equations (PDE) (see [1—5] and the references therein).展开更多
Let V0=diag（d1,…, dN）, V1=((1-δij)uij), where di are the distinct complex constants and the potentials uij=uij（x, t） are taken from the Schwartz space S for the fixed t. Set x0=1, x1=x, and define the matrices W...Let V0=diag（d1,…, dN）, V1=((1-δij)uij), where di are the distinct complex constants and the potentials uij=uij（x, t） are taken from the Schwartz space S for the fixed t. Set x0=1, x1=x, and define the matrices Wkα, k=0, 1, 2,…; α=0,1, by W0α=xαV0, W1α=xαV1, aδj0V0-Wjxα+[V0, Wj+1α]+[V1, Wjα]=0, j≥0,展开更多
Theorem 2. The infinitesimal Backlund transformnations Bλ+εBγ-1 of the sine-Gordon equation are permutable if and only if the conserred densities of the equation are in involution in pairs. This theorem reveals an ...Theorem 2. The infinitesimal Backlund transformnations Bλ+εBγ-1 of the sine-Gordon equation are permutable if and only if the conserred densities of the equation are in involution in pairs. This theorem reveals an intrinsie展开更多
The most time-consuming part in many systematic and applied softwares such as data processing, compiling or assembling is to compare an external symbol with internal ones which are always arranged previously into some...The most time-consuming part in many systematic and applied softwares such as data processing, compiling or assembling is to compare an external symbol with internal ones which are always arranged previously into some table. By means of such comparisions one can finally identify the external symbol, and then get some necessary infor-展开更多
基金The project supported by National Natural Science Foundation Committeethrough Nankai Institute of Mathematics
文摘An isospectral problem with four potentials is discussed. The corresponding hierarchy of nonlinearevolution equations is derived. It is shown that the AKNS, Levi, D-AKNS hierarchies and a new oneare reductions of the above hierarchy. In each case the relevant Hamiltonian form is established bymaking use of the trase identity.
基金Project supported by the National Natural Science Foundation of China.
文摘On the basis of an analysis of the loop algebra ?_1 a new hierarchy of integrable sys-tems is proposed. The Hamiltonian structure of the new hierarchy of equations is established by means of constrained formal variational calculus. This hierarchy of evolution equations is demonstrated to possess an infinite number of conserved densities, which are ininvolution in pairs.
基金Project supported by the National Natural Science Foundation of China
文摘The background of the present investigation is the Darboux transformation (DT),which is nowadays an effective method in generating solutions of partial differential equations (PDE) (see [1—5] and the references therein).
文摘Let V0=diag（d1,…, dN）, V1=((1-δij)uij), where di are the distinct complex constants and the potentials uij=uij（x, t） are taken from the Schwartz space S for the fixed t. Set x0=1, x1=x, and define the matrices Wkα, k=0, 1, 2,…; α=0,1, by W0α=xαV0, W1α=xαV1, aδj0V0-Wjxα+[V0, Wj+1α]+[V1, Wjα]=0, j≥0,
文摘Theorem 2. The infinitesimal Backlund transformnations Bλ+εBγ-1 of the sine-Gordon equation are permutable if and only if the conserred densities of the equation are in involution in pairs. This theorem reveals an intrinsie
文摘The most time-consuming part in many systematic and applied softwares such as data processing, compiling or assembling is to compare an external symbol with internal ones which are always arranged previously into some table. By means of such comparisions one can finally identify the external symbol, and then get some necessary infor-
