March 17 Math Colloquium
Baofeng Feng, University of Texas Rio Grande Valley
KP-Toda hierarchy reduction method for soliton equations
We give a review for the KP-Toda hierarchy reduction method to find multi-soliton and rogue wave solutions to soliton equations which was developed by Kyoto School. The KP- Toda hierarchy reduction method usually starts with the bilinear equations satisfied by the tau functions of the KP-Toda hierarchy, then through a series of reductions such as dimension and symmetry reductions, finally the multi-soliton or rogue wave solution can be derived in either determinant or Pfaffian form. In this talk, I will take the nonlinear Schrodinger (NLS) equation and its vector form as an example to show how we can derive the multi-bright, multi-dark and mixed soliton solutions. If time permits, I will report nonsingular soliton solutions with zero and nonzero boundary conditions to a nonlocal NLS equation with PT-symmetry.
This is a joint work with Mark Ablowitz, Yasuhiro Ohta and Kenichi Maruno.