Soliton scattering with amplitude changes of a negative order AKNS equation

The paper investigates a nonlinear model which provides soliton scattering with amplitude changes. This is a nonlinear equation in negative order AKNS hierarchy. We derive its N -soliton solutions through Hirota method. For dynamics, 1-soliton is characterized by an asymmetric shape and time-dependent amplitude. Then by means of asymptotic analysis it is found that two-soliton scattering provides not only phase shifts but also amplitude changes for each soliton, which differs from classical soliton interactions where only phase shifts appear. Appendix A gives a tentative discussion on Lax integrability and formal Hamiltonian structures of the negative order hierarchy, and Appendix B lists reductions of equations and solutions.