2013/12/19 by Ryan Croke, Croke, Ryan, Jennifer L. Mueller +9
Physics and Astronomy · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Advanced Fiber Laser Technologies
paper · pdf · doi:10.48550/arxiv.1312.5427
Recent progress in the theory and computation for the Novikov-Veselov (NV) equation is reviewed with initial potentials decaying at infinity, focusing mainly on the zero-energy case. The inverse scattering method for the zero-energy NV equation is presented in the context of Manakov triples, treating initial data of conductivity type rigorously. Special closed-form solutions are presented, including multisolitons, ring solitons, and breathers. The computational inverse scattering method is used to study zero-energy exceptional points and the relationship between supercritical, critical, and subcritical potentials.