Radiation of solitons described by a high-order cubic nonlinear Schrodinger equation
The resonant radiation of solitons due to higher order dispersion, described by an extended nonlinear Schrodinger (NLS) equation with nonlinear (cubic) dispersive terms and linear terms with third and fourth derivatives, is studied. The basic equation includes, as a particular case, a higher order derivative NLS equation. General properties of the master equation, such as conservation laws, Hamiltonian structures (in important particular cases), and Galilei transformation are studied. Explicit asymptotic expressions, describing the radiation at different initial conditions, are derived. The obtained results, in particular, provide a basis for the study of soliton losses, caused by the radiation, in optical fibers.
Karpman
VI
Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel.