Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation

We construct all higher order conserved charges from a general two-dimensional zero curvature condition using a Gardner transformation. Employing twoof those charges in the definition of a Hamiltonian allows to view theHirota equationsas an integrablePT-symmetric extension of the nonlinear Schrödinger equation. Weconstruct new degenerate multi-soliton solutions from Hirota’sdirect method as well asDarboux-Crum transformations based on Jordan states. We study the properties of thesesolutions, computing their asymptotic time-dependent displacements and also show thattheir scattering process has a distinct characteristic behaviour different from the nonde-generate counterparts allowing only for interactions of absorb-emit type