Perturbation theory for nearly integrable multi-component nonlinear PDEs

Details Perturbation theory for nearly integrable multi-component nonlinear PDEs Perturbation theory for nearly integrable multi-component nonlinear PDEs

2001-10-17

arxiv.org/abs/nlin/0110029v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Submitted to Journal of Mathematical Physics (References are corrected)

Scientific paper

The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary perturbations and is given in the form of exact equations, which generate the sequence of approximate ODEs in successive orders with respect to the perturbation. For vector nearly integrable PDEs, embracing the vector NLS and complex modified KdV equations, the main result is formulated in a theorem. For a single vector soliton the evolution equations for the soliton parameters and first-order radiation are given in explicit form

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