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1.
Jing Yu Jingwei Han Chuanzhong Li 《Mathematical Methods in the Applied Sciences》2020,43(6):3076-3085
For the orthosymplectic Lie superalgebra , we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures. 相似文献
2.
A method for the construction of the second constant of motion in fourth order is carried out. Correspondingly the fourth order potential equation is obtained whose solutions directly provide the classical integrable systems. Second constant of motion is obtained for a large class of potentials. Quantum invariants are also obtained with second order quantum corrections of the order O(?2) to the corresponding classical invariants. The phase space diagrams for these cases are drawn using a mathematical computer software package in two dimensions. 相似文献
3.
Jingsong He Kelei Tian Angela Foerster Wen-Xiu Ma 《Letters in Mathematical Physics》2007,81(2):119-134
Based on the Orlov and Shulman’s M operator, the additional symmetries and the string equation of the CKP hierarchy are established, and then the higher order
constraints on L
l
are obtained. In addition, the generating function and some properties are also given. In particular, the additional symmetry
flows form a new infinite dimensional algebra , which is a subalgebra of W
1+∞.
相似文献
4.
A new supersymmetric equation is proposed for the Sawada-Kotera equation. The integrability of this equation is shown by the existence of Lax representation and infinite conserved quantities and a recursion operator. 相似文献
5.
T. Kanna M. Lakshmanan 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):249-254
Soliton interactions in systems modelled by coupled nonlinear Schr?dinger (CNLS) equations and encountered in phenomena such
as wave propagation in optical fibers and photorefractive media possess unusual features: shape changing intensity redistributions,
amplitude dependent phase shifts and relative separation distances. We demonstrate these properties in the case of integrable
2-CNLS equations. As a simple example, we consider the stationary two-soliton solution which is equivalent to the so-called
partially coherent soliton (PCS) solution discussed much in the recent literature.
Received 1st October 2001 / Received in final form 4 February 2002 Published online 2 October 2002
RID="a"
ID="a"e-mail: lakshman@bdu.ernet.in 相似文献
6.
V.S. Gerdjikov 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):237-241
We compare the Hamiltonian properties of the N-soliton solutions of the NLSE in the adiabatic approximation and show how it matches the Hamiltonian formulation for the
complex Toda chain which describes the adiabatic N-soliton interactions.
Received 21 October 2001 Published online 2 October 2002
RID="a"
ID="a"e-mail: gerjikov@inrne.bas.bg 相似文献
7.
Ming-Hsien Tu 《Letters in Mathematical Physics》2007,81(2):93-105
We give an alternative proof of the Adler–Shiota–van Moerbeke formula for the BKP hierarchy. The proof is based on a simple
expression for the generator of additional symmetries and the Fay identity of the BKP hierarchy.
相似文献
8.
We study exactly the solvable noncommutative scalar quantum field models of (2n) or (2n + 1) dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B. 0 = 4-1 in field theoretic context means the full restoration of the maximal U(∞) gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable noncommutative φ4 quantum field model closely related to the 1+1-dimensional Moyal/matrix-valued nonlinear Schr6dinger (MNLS) equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly. 相似文献
9.
A practicable way to construct discrete integrable couplings is proposed by making use of two types of semi-direct sum Lie algebras. As its application, two kinds of discrete integrable couplings of the Volterra lattice are worked out. 相似文献
10.
D.G. Nomikos 《Physica D: Nonlinear Phenomena》2009,238(3):273-289
We study the Anisotropic Stormer Problem (ASP) and the Isosceles Three-Body Problem (IP), from the viewpoint of integrability, using Morales-Ramis theory and its generalization. The study of their integrability presents particular interest since they model important physical phenomena. Both problems can be reduced with respect to the S1 symmetry. Almeida and Stuchi [M.A. Almeida, T.J. Stuchi, Non-integrability of the anisotropic Stormer problem with angular momentum, Physica D 189 (2004) 219-233] proved that the reduced ASP is non-integrable for almost all values of the parameters. In this paper we establish the non-integrability (in the extended Liouville sense) of the remaining cases. The IP is a special case of the three-body problem and it can be considered as a generalization of the Sitnikov problem. Here we prove that the complexified reduced IP does not admit an additional independent meromorphic first integral. 相似文献