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D.E. Pelinovsky and C. Sulem

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Bifurcations of new eigenvalues for the Benjamin-Ono equation

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J. Math. Phys. 39, 6552-6572 (1998)

**Abstract:**

A criterion for the emergence of new eigenvalues is found for
the linear scattering problem associated with the Benjamin-Ono
(BO) equation. This bifurcation occurs
due to perturbations of nongeneric potentials which include the
soliton solutions of the BO equation. The asymptotic approximation
of an exponentially small new
eigenvalue is derived. The method is based on the expansion of
a localized function through a complete set of unperturbed
eigenfunctions. Explicit expressions are
obtained for the soliton potentials.

**Keywords:**

INITIAL-VALUE PROBLEM, SCATTERING TRANSFORM