Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.

💡 Research Summary

The paper develops a complete inverse scattering transform (IST) framework for the two‑component Camassa‑Holm system (CH2), which extends the celebrated Camassa‑Holm (CH) equation by coupling the momentum variable (m = u - u_{xx}) with an additional scalar field (\rho). The CH2 equations are written as
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