We prove that the τ-function of the integrable discrete sine-Gordon model apart from the " standard " bilinar identities obeys a number of " non-standard " ones. They can be combined into a bivector 3-dimensional difference equation which is shown to contain Hirota's difference analogue of the sine-Gordon equation and both auxiliary linear problems for it. We observe that this equation is most ...

A method of averaging is applied to study the dynamics of a kink in the damped double sine-Gordon equation driven by both external (nonparametric) and parametric periodic forces at high frequencies. This theoretical approach leads to the study of a double sine-Gordon equation with an effective potential and an effective additive force. Direct numerical simulations show how the appearance of two...

Abstract The primary object of study is the “cosine-sine” functional equation f ( xy ) = x g y )+ h for unknown functions f, g, : S → ℂ, where a semigroup. name refers to fact that it contains both sine and cosine addition laws. This has been solved on groups semigroups generated by their squares. Here we find solutions larger class discuss obstacles finding general solution all semigroups. Exa...

In order to characterize the creep behaviors of 2219 aluminum alloy at different temperatures and stress levels, a RWS-50 Electronic Creep Testing Machine (Zhuhai SUST Electrical Equipment Company, Zhuhai, China) was used for creep experiment at temperatures of 353~458 k and experimental stresses of 130~170 MPa. It was discovered that this alloy displayed classical creep curve characteristics i...

In one spatial dimension, a class of integrable manybody systems are the Calogero-Sutherland-Moser systems. They consist of many identical non-relativistic particles interacting through two-body potentials of the inverse square type and various extensions such as the inverse sine squared, the inverse hyperbolic squared, and the inverse squared Jacobian elliptic function [1 – 3]. The significanc...