Evolution of nonsoliton and quasi-classical wavetrains in nonlinear Schro¨dinger and Korteweg-de Vries equations with dissipative perturbations

摘要: Abstract Nonlinear Schrodinger equations “with attraction” and repulsion” (NSE(+) NSE(−)) the Korteweg-de Vries equation perturbed by small dissipative terms are considered. Near linear instability threshold, where nonlinear spatially nonuniform dissipations dominate, explicit solutions expressing local amplitude occupation numbers of a nonsoliton (dispersive) wavetrain in arbitrary initial data obtained, at sufficiently large times, logarithmic approximation. For NSE(+) particular case near soliton-birth threshold is also The influence dissipation on evolution “quasi-classical” (strongly nonlinear) studied. It demonstrated that for NSE(−) can be taken into account within framework eikonal approximation, while perturbation theory based inverse scattering transform relevant.