Deriving N-soliton solutions via constrained flows

The soliton equations can be factorized by two commuting x- and t-constrained flows. We propose a method to derive N-soliton solutions of soliton equations directly from the x- and t-constrained flows.Comment: 8 pages, AmsTex, no figures, to be published in Journal of Physics

Constructing N-soliton solution for the mKdV equation through constrained flows

Based on the factorization of soliton equations into two commuting integrable x- and t-constrained flows, we derive N-soliton solutions for mKdV equation via its x- and t-constrained flows. It shows that soliton solution for soliton equations can be constructed directly from the constrained flows.Comment: 10 pages, Latex, to be published in "J. Phys. A: Math. Gen.

Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians

The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems under study include the shallow water equation and Dym type equation. The classes of solutions are described in terms of theta-functions and their singular limits by using new parameterizations. A qualitative description of real valued solutions is provided

Unlocking the energy capabilities of micron-sized LiFePO4

Utilization of LiFePO4 as a cathode material for Li-ion batteries often requires size nanonization coupled with calcination-based carbon coating to improve its electrochemical performance, which, however, is usually at the expense of tap density and may be environmentally problematic. Here we report the utilization of micron-sized LiFePO4, which has a higher tap density than its nano-sized siblings, by forming a conducting polymer coating on its surface with a greener diazonium chemistry. Specifically, micron-sized LiFePO4 particles have been uniformly coated with a thin polyphenylene film via the spontaneous reaction between LiFePO4 and an aromatic diazonium salt of benzenediazonium tetrafluoroborate. The coated micron-sized LiFePO4, compared with its pristine counterpart, has shown improved electrical conductivity, high rate capability and excellent cyclability when used as a \u27carbon additive free\u27 cathode material for rechargeable Li-ion batteries. The bonding mechanism of polyphenylene to LiFePO4/FePO4 has been understood with density functional theory calculations