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【期刊论文】Energy-dependent third-order Lax operators
刘青平, M Antonowicz, A P Fordy and Q P Liu
Nonlinearity 4 (1991) 669-684. Printed in the UK,-0001,():
-1年11月30日
We consider an energy-dependent version of the third-order scalar Lax operator, thus extending our previous results. Unlike the second-order case it is no longer possible to expand the potentials as arbitrary polynomials in b. We prove that there are exactly four cases. We present Hamiltonian operators, Hamiltonian Miura maps and modifications for two new examples.
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刘青平, Q. P. Liu
J. Math. Phys. 37 (5), May 1996,-0001,():
-1年11月30日
The Hamiltonian theory for the two-component AKNS hierarchy and Yajima–Oikawa hierarchy is considered from the viewpoint of reduction. We show that the second Hamiltonian structures of the former is a Dirac reduction of the sl (3) current algebra, while the latter is related to the classical W4 ~3! algebra. © 1996 American Institute of Physics. [S0022-2488(96)01905-8]
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【期刊论文】Darboux Transformations for Supersymmetric Korteweg-de Vries Equations
刘青平, Q. P. LIU
Letters in Mathematical Physics 35: 115-122, 1995.,-0001,():
-1年11月30日
We consider the Darboux type transformations for the spectral problems of supersymmetric KdV systems. The supersymmetric analogies of Darboux and Darboux-Levi transformations are established for the spectral problems of Manin-Radul-Mathieu sKdV and Manin-Radul sKdV. Sevetral Backlund transformations are derived for the MRM sKdV and MR sKdV systems.
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【期刊论文】Miura map between lattice Kadomtsev–Petviashvili and its modification is canonical
刘青平, Q. P. Liu
JOURNAL OF MATHEMATICAL PHYSICS VOLUME 42, NUMBER 5, MAY 2001,-0001,():
-1年11月30日
We consider the Miura map between the lattice Kadomtsev–Petviashvili hierarchy and the lattice modified KP hierarchy and prove that the map is canonical not only between the first Hamiltonian structures, but also between the second Hamiltonian structures. © 2001 American Institute of Physics. [DOI: 10.1063/1.1359416]
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【期刊论文】Supersymmetric modified Korteweg–de Vries equation: bilinear approach
刘青平, Q P Liu, Xing-Biao Hu, and Meng-Xia Zhang,
Institute of Physics Publishing Nonlinearity Nonlinearity 18 (2005) 1597-1603,-0001,():
-1年11月30日
A proper bilinear form is proposed for the N=1 supersymmetric modified Korteweg–de Vries equation. The bilinear Backlund transformation for this system is constructed. As applications, some solutions are presented for it.
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