A Hamiltonian structure is presented, which generalizes classical Hamiltonian structure, by assigning a distinct symplectic operator for each unbounded space direction and time, of a Hamiltonianâ€¦ (More)

This paper and Part 2 report various new insights into the classic Kelvinâ€“Helmholtz problem which models the instability of a plane vortex sheet and the complicated motions arising therefrom. Theâ€¦ (More)

The paper provides an introduction and survey of conservative discretization methods for Hamiltonian partial differential equations. The emphasize is on variational, symplectic and multi-symplecticâ€¦ (More)

The linear stability problem for the Hockingâ€“Stewartson pulse, obtained by linearizing the complex Ginzburgâ€“Landau (cGL) equation, is formulated in terms of the Evans function, a complex analyticâ€¦ (More)

The linear stability problem for solitary wave states of the Kawaharaâ€”or fifthorder KdV-typeâ€”equation and its generalizations is considered. A new formulation of the stability problem in terms of theâ€¦ (More)

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 whoseâ€¦ (More)

The most eeective and widely used methods for integrating the Orr-Sommerfeld equation by shooting are the continuous orthogonalization method and the compound matrix method. In this paper, weâ€¦ (More)

The linear stability of solitary-wave or front solutions of Hamiltonian evolutionary equations, which are equivariant with respect to a Lie group, is studied. The organizing centre for the analysisâ€¦ (More)

The relationship between potential vorticity (PV) and the symplectic form is explored, for the shallow-water equations governing Lagrangian particle paths. Starting with the symplectic form, the PVâ€¦ (More)