We propose a mechanism for fixing the velocity of relativistic soliton based on the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal is first elaborated for a molecular chain model, as the simple pendulum limit of a double pendulums chain. It is then generalized to a full class of two-dimensional field theories of the sine-Gordon type. From a phenomenological point o...

In Part I (G. Olshanski) and Part II (A. Borodin) we developed an approach to certain probability distributions on the Thoma simplex. The latter has infinite dimension and is a kind of dual object for the infinite symmetric group. Our approach is based on studying the correlation functions of certain related point stochastic processes. In the present paper we consider the so–called tail point p...

The massive soliton theories describe integrable perturbations of WZW cosets as generalized multi-component sine-Gordon models. We study their coupling to 2-dim gravity in the conformal gauge and show that the resulting models can be interpreted as conformal non-Abelian Toda theories when a certain algebraic condition is satisfied. These models, however, do not provide quantum mechanically cons...

In this paper, with the aid of Maple, the (G ′ /G) and (1/G ′ )-expansion methods are applied to determine the exact solutions of (N+1)-dimensional generalized Boussinesq equation and (N+1)-dimensional sine-cosine-Gordon equation.These equations play a very important role in mathematical physics and engineering sciences. This methods are more powerful and will be used in further works to establ...

The limit distributions as T → ∞ of the functional ∫ T 0 f(X (t)) dt=T are found for onedimensional null-recurrent Markov processes X (t) under di erent assumptions concerning local characteristics of X (t) and f. The conditions for the convergence of the distribution of this functional to each distribution in the class of generalized arc-sine law, studied by Lamperti and Watanabe, are obtained...

The Clenshaw Curtis method for numerical integration is extended to semiinfinite ([_0, 30] and infinite [-0% oc] intervals. The common framework for both these extensions and for integration on a finite interval is to (1) map the integration domain to tc[0, z], (2) compute a Fourier sine or cosine approximation to the transformd integrand via interpolation, and (3) integrate the approximation. ...

A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Sync...

We develop the analytical theory of multikinks for strongly dispersive nonlinear systems, considering the examples of the weakly discrete sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise parabolic potential. We reveal that there are no 2p kinks for this model, but there exist discrete sets of 2pN kinks for all N.1. We also show their bifurcation structure in driven...

The capability of Extended tanh–coth, sine–cosine and Exp-Function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed. In this study, the generalized nonlinear Schrödinger (GNLS) equation is solved by three different methods. To obtain the single-soliton solutions for the equation, t...