Effective dynamics of double solitons for perturbed mKdV

Abstract

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.

The numerical illustrations of the results and MATLAB codes can be found at http://math.berkeley.edu/~zworski/hpzweb.html

References in corpus (4)

• Solitary Wave Dynamics in an External Potential
• Asymptotic stability of N-soliton states of NLS
• On the soliton dynamics under a slowly varying medium for generalized KdV equations
• Stability of two soliton collision for nonintegrable gKdV equations

Cited by in corpus (2)

• Soliton interaction with small Toeplitz potentials for the Szego equation on the real line
• Effective dynamics for $N$-solitons of the Gross-Pitaevskii equation