Asymptotic stability of the Toda m-soliton

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:386

Article

Benes, G. N.^2,3  Hoffman, A.¹  Wayne, C. E.^2,3 

[1] Franklin W Olin Coll Engn, Needham, MA 02492 USA

[2] Boston Univ, Ctr BioDynam, Boston, MA 02215 USA

[3] Boston Univ, Dept Math & Stat, Boston, MA 02215 USA

关键词: Lattice differential equation;    Toda lattice;    Soliton;    Stability;    Backlund transform;   

DOI  :  10.1016/j.jmaa.2011.08.007

来源: Elsevier

【 摘 要 】

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 Backlund 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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