Boundary conditions changing operators have played an important role in conformal field theory. Here, we study their equivalent in the case where a mass scale is introduced, in an integrable way, either in the bulk or at the boundary. More precisely, we propose an axiomatic approach to determine the general scalar products b θ ′ n a between asymptotic states in the Hilbert spaces with a and b b...

1. Introduction In the past few years, computation of definite integrals to high precision has emerged as a very useful tool in experimental mathematics. In particular, it is often possible to recognize an otherwise unknown definite integral in analytic terms, provided its numerical value can be calculated to high accuracy. As a single example, recently the author, together with Jonathan Borwei...

We consider an (n+1)-dimensional q-deformed double sinh-Gordon equation. The dynamical system approach is employed to study the model problem, from which we are able obtain all possible bounded solutions, such as solitary wave kink and anti-kink periodic solutions under different parameter conditions. Eleven exact parametric representations provided explicitly.

In this article, a new version of the generalized q-deformed Sinh–Gordon equation is presented, and analytical solutions are developed for specific parameter sets using those equations. There possibility that can be used to model physical systems have broken symmetries include also effects related amplification or dissipation. addition, we some illustrations depict varied patterns soliton propa...

Due to the nonvanishing average photon population of the squeezed vacuum state, finite corrections to the scattering matrix are obtained. The lowest order contribution to the electron mass shift for a one mode squeezed vacuum state is given by δm(Ω, s)/m = α(2/π)(Ω/m) sinh(s), where Ω and s stand for the mode frequency and the squeeze parameter and α for the fine structure constant, respectivel...

In this study, we applied the generalized Kudryashov method to two different conformable fractional differential equations and one system namely Burgers’ equation with derivative, Wu-Zhang sinh-Gordon equation. Obtained solutions are soliton-type solutions. All obtained have been verified considered correct by placing them in original help of Maple software program. Also, plotted three-dimensio...

The authors offer a unified method extending traditional spatial dependence with normally distributed error terms to a new class of spatial models based on the biparametric exponential family of distributions. Joint modeling of the mean and variance (or precision) parameters is proposed in this family of distributions, including spatial correlation. The proposed models are applied for analyzing...

For a particular class of integral operators K we show that the quantity φ := log det (I +K)− log det (I −K) satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

We propose a class of double hierarchical generalized linear models in which random effects can be specified for both the mean and dispersion. Heteroscedasticity between clusters can be modelled by introducing random effects in the dispersion model, as is heterogeneity between clusters in the mean model.This class will, among other things, enable models with heavy-tailed distributions to be exp...