Related papers: Dispersionless BKP Hierarchy and Quadrant L\"owner…

Recently, it was shown that in inclusive B -> Xs l+ l- decay, an angular decomposition provides three independent (q^2 dependent) observables. A strategy was formulated to extract all measurable Wilson coefficients in B -> Xs l+ l- from a…

We present a systematic way to construct solutions of the (n=5)-reduction of the BKP and CKP hierarchies from the general tau function of the KP hierarchy. We obtain the one-soliton, two-soliton, and periodic solution for the bi-directional…

We describe a calculation of the fully-differential decay rate of a top quark to a massless $b$-quark and a lepton pair at next-to-next-to-leading order in perturbative QCD. Technical details of the calculation are discussed and selected…

We compare the factorization approach, the perturbative QCD approach and the Beneke-Buchalla-Neubert-Sachrajda approach to nonleptonic charmless $B$ meson decays. We discuss their treatments of factorizable, nonfactorizable, and…

The existence of decompositions of the nonlinear integrable systems not only permits us to establish so-called linear superposition solutions but also to derive new nonlinear integrable coupled systems. Restricting our attention to the…

We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.

We study the nonleptonic charmless $B_{u,d,s} \to K_0^*(1430)P$ $(P=K\,, \pi)$ and $ K_0^*(1430)V$ $ (V=K^*\,, \rho\,, \omega\,, \phi)$ decays. The amplitudes are calculated within the QCD factorization, and the non-perturbative quantities…

A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…

In this paper, we prove the reducibility for some linear quasi-periodic Hamiltonian derivative wave and half-wave equations under the Brjuno-R\"{u}ssmann non-resonance conditions. This generalizes KAM theory by P\"{o}schel in [38] from the…

We study the variational structure of the discrete Kadomtsev-Petviashvili (dKP) equation by means of its pluri-Lagrangian formulation. We consider the dKP equation and its variational formulation on the cubic lattice ${\mathbb Z}^{N}$ as…

The so-called KP-mKP hierarchy, which was introduced recently via pseudo-differential operators with two derivations, can be reduced to the Kadomtsev-Petviashvili (KP), the modified KP (mKP) and the two-component BKP hierarchies. In this…

We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…

The simplest non-trivial solutions of WDVV equations are A_n and B_n-potentials, which describe metrics of K.Saito on spaces of versal deformation of A_n and B_n-singularities. These are some polynomials, which were known for $n\leqslant$…

We consider elliptic solutions of the semi-discrete BKP equation and derive equations of motion for their poles. The basic tool is the auxiliary linear problem for the wave function.

We analyze the $B\to K_2^*(\to K\pi)l^+l^-$ (with $l=e,\mu,\tau$) decay in the standard model and two new physics scenarios: vector-like quark model and family non-universal $Z'$ model. We derive its differential angular distributions,…

We construct a new multi-component CKP hierarchy based on the eigenfunction symmetry reduction. It contains two types of CKP equation with self-consistent sources which Lax representations are presented. Also it admits reductions to…

This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of "Landau-Ginzburg potentials" that play the role of reduced Lax…

We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with…

Inspired by the brilliant prospects of the ongoing $B$ meson experiments, the hadronic charmless $B$ ${\to}$ $SS$ decays are studied by considering the next-to-leading (NLO) contributions with the QCD factorization approach, where $S$…

We have recently solved the inverse spectral problem for integrable PDEs in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter $\lambda$. The associated inverse problem, in…