We have recently solved the inverse scattering problem for oneparameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev Petviashvili (dKP) equation. We showed, in particu...

It is shown that Einstein–Weyl (EW) equations in 2+1 dimensions contain the dispersionless Kadomtsev–Petviashvili (dKP) equation as a special case: If an EW structure admits a constant weighted vector then it is locally given by h = dy2−4dxdt−4udt2, ν = −4uxdt, where u = u(x, y, t) satisfies the dKP equation (ut − uux)x = uyy. Linearised solutions to the dKP equation are shown to give rise to f...

We review briefly some ideas and constructions for dKP (from KP) and its Hamiltonian dynamics, discuss its quantization via Moyal back to KP, and treat the KP hierarchy itself as a sequence of quantum Hamiltonian systems based on the dKP dynamics. Some connections to q-theories are also indicated. The constructions are all well known (cf. [6, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 29, 3...

Recently the study of Fay-type identities revealed some new features of the DKP hierarchy (also known as “the coupled KP hierarchy” and “the Pfaff lattice”). Those results are now extended to a Toda version of the DKP hierarchy (tentatively called “the Pfaff–Toda hierarchy”). Firstly, an auxiliary linear problem of this hierarchy is constructed. Unlike the case of the DKP hierarchy, building bl...

THE TITLE COMPOUND [SYSTEMATIC NAME: (8S)-8-methyl-6,9-diaza-spiro-[4.5]decane-7,10-dione], C(9)H(14)N(2)O(2), consists of two connected rings, viz. a piperazine-2,5-dione (DKP) ring and a five-membered ring. The DKP ring adopts a slight boat conformation and the bonded methyl group is in an equatorial position. The five-membered ring is in an envelope conformation. In the crystal structure, in...

We present a two-layer architecture for two-wheeled robots trajectory planning. This architecture can be used to describe steering behaviours and to generate candidate trajectories that will be evaluated by a higher-level layer before choosing which one will be followed. The higher layer uses a TÆMS tree to describe the current robot goal and its decomposition into alternative steering behaviou...

The Clifford algebraic formulation of the Duffin–Kemmer–Petiau (DKP) algebras is applied to recast De Donder–Weyl Hamiltonian (DWH) theory as an description independent matrix representation DKP algebra. We show that DWH equations for antisymmetric fields arise out action algebra on certain invariant subspaces which carry representations fields. representation-free formula bracket associated wi...

The generalized Duffin-Kemmer-Petiau (DKP) oscillator with electromagnetic interactions in the curved space-times are investigated. We introduce firstly DKP Som-Raychaudhuri space-time Cornell potential. Then, we consider into oscillator. energy eigenvalues and eigenfunction of our problem obtained. effect from parameters space-time, frequency oscillator, potential magnetic flux on have been an...

In this paper, we investigate the modification of gravitational fields generated by topological defects on a generalized Duffin–Kemmer–Petiau (DKP) oscillator for spin-0 particle under spinning cosmic string background. The DKP equation background is established, and impact Cornell potential presented. We give influence space-time parameters energy levels.

This study examines the properties of a 4 × 2 matrix of aqueous cations and anions at concentrations up to 8.0 M. The apparent molar water volume, as calculated by subtracting the mass and volume of the ions from the corresponding solution density, was found to exceed the molar volume of ice in many concentrated electrolyte solutions, underscoring the nonideal behavior of these systems. The sol...