Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-Gördon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren’t true. In final, we prove that our solutions to Sinh-Görd...

We examine the behaviour of the maximally entangled Bell state of two spin 12 massive particles under relativistic transformations. On the basis of explicit calculations of the Wigner rotation and the use of transformation properties of Dirac spinors, we establish that the constituent particles of the Bell state undergo momentum dependent rotation of the spin orientations characterized by the W...

We study the noncommutative generalization of (euclidean) integrable models in two-dimensions, specifically the sine-and sinh-Gordon and the U (N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its na¨ıve noncommutative generalization is not integrable. On the other hand, the addition of extra constraints, obtained through the generalization ...

We study the noncommutative generalization of (euclidean) integrable models in two-dimensions, specifically the sine-and sinh-Gordon and the U (N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its na¨ıve noncommutative generalization is not integrable. On the other hand, the addition of extra constraints, obtained through the generalization ...

A new kind of numerical method based on rational spectral collocation with the sinh transformation is presented for solving parameterized singularly perturbed two-point boundary value problems with one boundary layer. By means of the sinh transformation, the original Chebyshev points are mapped onto the transformed ones clustered near the singular points of the problem. The results from asympto...

We will mainly consider the Sinh-Gordon model in finite spacial volume which corresponds to imposing the periodic boundary conditions φ(x + R) = φ(x). A lot is known about the Sinh-Gordon model in infinite volume R → ∞, see e.g. [1, 2, 3, 4, 5]. The spectrum contains a single particle with mass m which is related to the parameter μ in (1.1) in a definite way [6], see eqn. (5.32) below. The S-ma...

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...

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...

We find that the fundamental quadratic form of classical string propagation in 2 + 1 dimensional constant curvature spacetimes solves the Sinh-Gordon equation, the Cosh-Gordon equation or the Liouville equation. We show that in both de Sitter and anti de Sitter spacetimes (as well as in the 2 + 1 black hole anti de Sitter spacetime), all three equations must be included to cover the generic str...

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.