Solitons of the nonlinear Schrödinger equation generated by the continuum (Q1089839)

The large time asymptotics of the solutions of a nonlinear Schrödinger equation (NS) which are approaching zero when \(x\to +\infty\) and a finite-gap solution of NS when \(x\to -\infty\) are investigated. It is proved that these solutions for \(t\to \infty\) are splitting into infinite series of solitons with variable phases. These solitons are generated by the continuous spectrum of the L-operator from the corresponding Lax representation.