In this article, we solve the Duffin--Kemmer--Petiau (DKP) equation in presence of hyperbolic tangent potential for spin-one particles. By partitioning spinor, show that DKP is equivalent to Klein--Gordon formalism. The scattering solutions are derived terms hypergeometric functions. reflection $R$ and transmission $T$ coefficients calculated Gamma results superradiance phenomenon when a specif...

We have recently solved the inverse spectral 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, arising as commutation ...

Vector couplings in the Duffin-Kemmer-Petiau theory are revised. It is shown that minimal and nonminimal vector potentials behave differently under charge-conjugation and time-reversal transformations. In particular, it is shown that nonminimal vector potentials have been erroneously applied to the description of elastic meson-nucleus scatterings and that the space component of the nonminimal v...

The presence of amino acids on the prebiotic Earth, either stemming from endogenous chemical routes or delivered by meteorites, is consensually accepted. Prebiotically plausible pathways to peptides inactivated are still unclear as most oligomerization approaches rely thermodynamically disfavored reactions in solution. Now, a combination prebiotically minerals and mechanochemical activation ena...

We have recently solved the inverse spectral 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, arising as commutation ...

A new universal strategy exploits DKP formation in a dipeptide moiety whose C-terminal residue is blocked by a leaving group. It enables both synthesis of C-terminal protected peptides that are useful for convergent synthesis of large peptides and use of a C-terminal permanent protecting group that can be cleaved by catalytic hydrogenation to release the peptide.

The factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is developed for the construction classes of nontrivial solutions of the dKP equation.

We review the notion of differential Fay identities and demonstrate, through case studies, its new role in integrable hierarchies of the KP type. These identities are known to be a convenient tool for deriving dispersionless Hirota equations. We show that differential (or, in the case of the Toda hierarchy, difference) Fay identities play a more fundamental role. Namely, they are nothing but a ...