摘 要: |
In this talk, we study the Cauchy problem for a coupled generalized nonlinear Schrödinger (cgNLS) equation. Using the D-bar generalization of the non-linear steepest descent method we compute the long-time asymptotic expansion of the solution in any fixed space-time cone up to an (optimal) residual error of order O(t^{−3/4}). In each cone the leading order term in this expansion is a multi-soliton whose parameters are modulated by soliton–soliton and soliton–radiation interactions as one moves through the cone. Our results require that the initial data possess one L^2(R) moment and (weak) derivative and that it not generate any spectral singularities. |