Biomedical subjects
Publications and source records attributed to K M Case.
Elucidating earlier work, it is shown that the Kadomtsev-Petviashvili equation has n + 2 constants for all n >/= 0. It also has a pseudo-constant from which the constants can be obtained by differentiation with respect to time. The pseudo-constant can be obtained from a basis functional J(n) ((n+2)) = -1/18 [unk] y(n+2)q by taking repeated Poisson brackets with the Hamiltonian.
A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.
Many nonlinear equations arising in plasma physics, hydrodynamics, and solid-state physics can be written in Hamiltonian form. The full advantage of this is achieved only when the existence of canonical coordinates and momenta is known. Here such coordinates are exhibited for three large classes of equations-which seem to include almost all known completely integrable Hamiltonian systems.
Conserved densities for Hamiltonian systems are shown to satisfy simple linear equations. These are essentially the original equations linearized around a particular solution. A number of examples are displayed, which pertain to many systems of physical interest.
A class of Bäcklund transformations for multidimensional sine-Gordon equations is shown to relate solutions of only one- and two-dimensional equations. Also, a proposed superposition principle is shown to be useless.
It is shown that the Benjamin-Ono equation is one of a hierarchy of nonlinear partial differential singular integral equations. Explicit multisoliton solutions are constructed for all equations of the hierarchy.
A theorem is deduced that reduces the problem of finding the N-soliton solution of the Benjamin-One equation to that of solving an algebraic equation of degree N.