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We consider the change in the asymptotic behavior of solutions of the type of flat domain walls (i.e., kink solutions) in field-theoretic models with a real scalar field. We show that when the model is deformed by a bounded deforming function, the exponential asymptotics of the corresponding kink solutions remain exponential, while the power-law ones remain power-law. However, the parameters of these asymptotics, which are related to the wall thickness, can change.
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We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon state is given by the same expression as the inner product of a 2M-magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular Lx2M grid, with partial domain-wall boundary conditions.
We study the asymptotic properties of kinks in connection with the deformation procedure. We show that, upon deformation of the field-theoretic model, the asymptotics of kinks can change or remain unchanged, depending on the properties of the deforming function. The cases of both explicit and implicit kinks are considered. In addition, we modified the algorithm for obtaining the deformed kink for the case of implicit kinks.
In this paper we study in detail the deformations introduced in [1] of the integrable structures of the AdS$_{2,3}$ integrable models. We do this by embedding the corresponding scattering matrices into the most general solutions of the Yang-Baxter equation. We show that there are several non-trivial embeddings and corresponding deformations. We work out crossing symmetry for these models and study their symmetry algebras and representations. In particular, we identify a new elliptic deformation of the $rm AdS_3 times S^3 times M^4$ string sigma model.
Motivated by the BPS/CFT correspondence, we explore the similarities between the classical $beta$-deformed Hermitean matrix model and the $q$-deformed matrix models associated to 3d $mathcal{N}=2$ supersymmetric gauge theories on $D^2times_{q}S^1$ and $S_b^3$ by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the $W$-algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.
We demonstrate that for some certain values of parameters of the $(1+1)$-dimensional $varphi^8$ model, the kink solutions can be found from polynomial equations. For some selected values of the parameters we give the explicit formulas for the kinks in all topological sectors of the model. Based on the obtained algebraic equations, we show that in a special limiting case, kinks with power-law asymptotics arise in the model, describing, in particular, thick domain walls. Objects of this kind could be of interest for modern cosmology.
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