Asymptotic Stability of the Toda m-Soliton2012
AbstractWe prove that multi-soliton solutions of the Toda lattice are both linearly and nonlinearly stable in exponentially weighted spaces. Our proof uses neither the inverse spectral method nor the Lax pair of the model but instead studies the linearization of the Bäcklund transformation which links the (m−1)-soliton solution to the m-soliton solution. We use this to construct a conjugation between the Toda flow linearized about an m-soliton solution and the Toda flow linearized about the zero solution, whose stability properties can be determined by explicit calculation.
Citation InformationG. Nicholas Benes, Aaron Hoffman and C. Eugene Wayne. "Asymptotic Stability of the Toda m-Soliton" (2012)
Available at: http://works.bepress.com/aaron_hoffman/17/