Gauge covariant theory of the generating operator. I |
| |
Authors: | V S Gerdjikov A B Yanovski |
| |
Institution: | (1) Joint Institute for Nuclear Research, Dubna, SU-101000 Moscow, USSR;(2) Present address: Institute of Nuclear Research and Nuclear Energy, Sofia, Bulgaria |
| |
Abstract: | A gauge covariant formulation of the generating operator ( -operator) theory for the Zakharov-Shabat system is proposed. The operator
, corresponding to the gauge equivalent system in the pole gauge is explicitly calculated. Thus the unified approach to the nonlinear Schrödinger-type equations based on is automatically reformulated with the help of
for the Heisenberg ferromagnet-type equations. Consequently, it is established that the conserved densities for the Heisenberg-ferromagnet-type equations are polynomial inS(x) and itsx-derivatives. Special attention is paid to the interrelation between the hierarchies of symplectic structures corresponding to the above mentioned families of gauge-equivalent equations. It is shown that the geometrical properties of the conjugated operator * are gaugeindependent. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|