Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations

A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described by Hamilton-Jacobi type equations associated with hierarchies of dispersionless integrable systems. These hierarchies are constructed by applying the quasiclassical $\bar{\partial}$-dressing method.Comment: 30 pages, tcilate

Integrable Quasiclassical Deformations of Algebraic Curves

A general scheme for determining and studying integrable deformations of algebraic curves is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of hydrodynamic type is characterized.Comment: 28 pages, no figure

Hydrodynamic reductions and solutions of a universal hierarchy

The diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains are explicitly characterized. Their compatibility with previously introduced reductions of differential type is analyzed and their associated class of hodograph solutions is discussed.Comment: 19 page

dbar-approach to the dispersionless KP hierarchy

The dispersionless limit of the scalar nonlocal dbar-problem is derived. It is given by a special class of nonlinear first-order equations. A quasi-classical version of the dbar-dressing method is presented. It is shown that the algebraic formulation of dispersionless hierarchies can be expressed in terms of properties of Beltrami tupe equations. The universal Whitham hierarchy and, in particular, the dispersionless KP hierarchy turn out to be rings of symmetries for the quasi-classical dbar-problem.Comment: 13 pages, LaTex 24.9K

Orbit transfer rocket engine technology program. Phase 2: Advanced engine study

In Phase 2 of the Advanced Engine Study, the Failure Modes and Effects Analysis (FMEA) maintenance-driven engine design, preliminary maintenance plan, and concept for space operable disconnects generated in Phase 1 were further developed. Based on the results of the vehicle contractors Orbit Transfer Vehicle (OTV) Concept Definition and System Analysis Phase A studies, minor revisions to the engine design were made. Additional refinements in the engine design were identified through further engine concept studies. These included an updated engine balance incorporating experimental heat transfer data from the Enhanced Heat Load Thrust Chamber Study and a Rao optimum nozzle contour. The preliminary maintenance plan of Phase 1 was further developed through additional studies. These included a compilation of critical component lives and life limiters and a review of the Space Shuttle Main Engine (SSME) operations and maintenance manual in order to begin outlining the overall maintenance procedures for the Orbit Transfer Vehicle Engine and identifying technology requirements for streamlining space-based operations. Phase 2 efforts also provided further definition to the advanced fluid coupling devices including the selection and preliminary design of a preferred concept and a preliminary test plan for its further development