turkmath.org

In this talk I review SL(2,R) AKNS and the Kaup-Newell integrable resonant soliton hierarchies and describe several new results and applications. The second flow of the hierarchies is related with resonant nonlinear Schrodinger equation (RNLS) and resonant DNLS equation in 1+1 dimensions, with de Broglie-Bohm quantum potential nonlinear term. Soliton interactions for the first equation show the resonance phenomena and for the second one, the chiral resonant soliton interaction. It is shown that in non-Madelung fluid representation, RNLS is connected with the Broer-Kaup resonant system. Combining the second and the third flows of the hierarchy we construct line solitons of KP-II and MKP-II equations in 2+1 dimensions with web type resonant structure. As a next natural generalization we discuss the resonant Davey-Stewartson equation, as 2+1 dimensional nonlocal RNLS and corresponding new integrable 2+1 dimensional Broer-Kaup type system. By the recursion operator of AKNS hierarchy, the non-local relativistic RNLS (DNLS) and q-dispersive resonant soliton equations are derived. New local relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions, gauge equivalent to Papanicolau spin model on one sheet hyperboloid is constructed. In terms of the so called double numbers, it is represented as hyperbolic complex relativistic massive Thirring model. By using Hirota bilinear method, exact one and two dissipaton solutions, showing resonant scattering of two soliton particles, with relativistic dispersion and highly nonlinear mass are obtained.

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1647243893612?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a49a1949-9464-4e2b-861d-221a6985322e%22%7d