A Hamiltonian-Krein (instability) index theory for KdV-like eigenvalue problems
نویسندگان
چکیده
The Hamiltonian-Krein (instability) index is concerned with determining the number of eigenvalues with positive real part for the Hamiltonian eigenvalue problem JLu = λu, where J is skewsymmetric and L is self-adjoint. If J has a bounded inverse the index is well-established, and it is given by the number of negative eigenvalues of the operator L constrained to act on some finite-codimensional subspace. There is an important class of problems namely, those of KdV-type for which J does not have a bounded inverse. In this paper we overcome this difficulty and derive the index for eigenvalue problems of KdV-type. We use the index to discuss the spectral stability of homoclinic traveling waves for KdV-like problems and BBM-type problems.
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