Mathematics – Analysis of PDEs
Scientific paper
2009-12-28
Mathematics
Analysis of PDEs
The numerical illustrations of the results and MATLAB codes can be found at http://math.berkeley.edu/~zworski/hpzweb.html
Scientific paper
We show that an interacting double soliton solution to the perturbed mKdV equation is close in $H^2$ to a double soliton following an effective dynamics obtained as Hamilton's equations for the restriction of the mKdV Hamiltonian to the submanifold of solitons. The interplay between algebraic aspects of complete integrability of the unperturbed equation and the analytic ideas related to soliton stability is central in the proof.
Holmer Justin
Perelman Galina
Zworski Maciej
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