We investigate the relationship between the nonlinear partial differential equations (PDEs) of mathematical physics and their linearizations around stationary localized solutions. It turns out that for the PDEs of sine-Gordon type, it is possible to solve the Inverse Linearization Problem, which is as follows: given linear stability analysis equations (LSAE) for an unknown PDE around an unknown stationary solution, restore the PDE. Of a particular interest are the instances of transparency of the LSAEs that may hint on the integrability of the corresponding PDEs.
Seminar Date:Monday, April 25 1:30pm - 6:15pm at Brown
Speaker:Maxim Olshanii (University of Massachusetts Boston)