4 research outputs found
Dressing chain equations associated to difference soliton systems
The dressing chain equations for factorizing operators of a spectral problem
are derived. The chain equations itselves yield nonlinear systems which closure
generates solutions of the equations as well as of the nonlinear system if both
operators of the correspondent Hirota bilinearization are covariant with
respect to Darboux transformation which hence defines a symmetry of the
nonlinear system as well as of these closed chains. Examples of Hirota and Nahm
equations are specified.Comment: 12 page
Nonlinear waves in waveguides: with stratification
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory