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The inverse linearization problem

Semester: 
Spring 2016
Seminar Date: 
Monday, April 25 1:30pm - 6:15pm at Brown
Speaker: 
Maxim Olshanii (University of Massachusetts Boston)

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.