Abstract
The spectral problem associated with the linearization about solitary waves of the generalized fifth-order KdV equation is
formulated in terms of the Evans function, a complex analytic function whose zeros correspond to eigenvalues. A numerical
framework, based on a fast robust shooting algorithm on exterior algebra spaces is introduced. The complete algorithm has
several new features, including a rigorous numerical algorithm for choosing starting values, a new method for numerical
analytic continuation of starting vectors, the role of the Grassmannian G2(C5) in choosing the numerical integrator, and the
role of the Hodge star operator for relating Ʌ2(C5) and Ʌ3(C5) and deducing a range of numerically computable forms for
the Evans function. The algorithm is illustrated by computing the stability and instability of solitary waves of the fifth-order
KdV equation with polynomial nonlinearity.