Discontinuous nonlinear evolution equations: Broken conservation laws and soliton tunnelling (Q1069363)

The problem of nonlinear evolution equations with discontinuous coefficients is investigated by extended use of the AKNS scheme [e.g.: \textit{M. Ablowitz}, Stud. Appl. Math. 58, 17-94 (1978; Zbl 0384.35019)] and of the associated conservation laws, in view of an analysis of soliton fission and tunnelling. The employment of the motion constants evaluated by the broken conservation laws in the description of a tunnelling process for a nonlinear Schrödinger equation with a potential-like term is illustrated by a numerical experiment.