Evolution of solitonless wave packets in the nonlinear Schrödinger equation and the Korteweg-de Vries equation with dissipative perturbations
Nonlinear Schrödinger (for both repulsive and attractive cases), Korteweg-de Vries and sine-Gordon equations with small dissipative perturbing terms are considered. Near the linear instability threshold, where nonlinear and spatially inhomogeneous dissipation dominates, explicit solutions expressing local amplitude and occupation numbers of a nonsoliton (dispersive) wavetrain in terms of arbitrary initial data are obtained at sufficiently large times in the logarithmic approximation. For the nonlinear Schrödinger equation with the repulsion, the particular case of the wavetrain near the soliton production threshold is also considered.
scientific article; zbMATH DE number 4002682