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Asymptotic Stability of the Toda m-Soliton
  • G. Nicholas Benes, Boston University
  • Aaron Hoffman, Franklin W. Olin College of Engineering
  • C. Eugene Wayne, Boston University
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We 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.

© 2012 Elsevier. This article was published in the Journal of Mathematical Analysis and Applications, vol. 386, iss. 1, pp. 445-460 and may be found here.

Citation Information
G. Nicholas Benes, Aaron Hoffman and C. Eugene Wayne. "Asymptotic Stability of the Toda m-Soliton" (2012)
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