We study relations of the Weierstrass’s hyperelliptic al-functions over a non-degenerated hyperelliptic curve y = f(x) of arbitrary genus g as solutions of sine-Gordon equation using Weierstrass’s local parameters, which are characterized by two ramified points. Though the hyperelliptic solutions of the sine-Gordon equation had already obtained, our derivations of them is simple; they need only...

The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim σ-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F ⊃ G ⊃ H . We show that for every symmetric space F/G, the generalized sine-Gordon models can be derived from the G/H WZW action, p...

We investigate bi–Hamiltonian structures and related mKdV hierarchy of solitonic equations generated by (semi) Riemannian metrics and curve flow of non–stretching curves. The corresponding nonholonomic tangent space geometry is defined by canonically induced nonlinear connections, Sasaki type metrics and linear connections. One yields couples of generalized sine–Gordon equations when the corres...

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...

We discuss the relationship between two-dimensional (2D) dilaton gravity models and sine-Gordon-like field theories. We show that there is a one-to-one correspondence between the solutions of 2D dilaton gravity and the solutions of a (two fields) generalization of the sine-Gordon model. In particular, we find a connection between the soliton solutions of the generalized sine-Gordon model and ex...

This paper considers the non-linear Kudryashov's equation, that is an extension of well-known dual-power law refractive index and analog to generalized version anti-cubic non-linearity. The model considered in presence full main objective this extract soliton solutions proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, sine-Gordon expansion me...

Abstract. We investigate the low-energy properties of a generalized quantum sine-Gordon model in one dimension with a self-dual symmetry. This model describes a class of quantum phase transitions that stems from the competition of different orders. This SU(N ) self-dual sine-Gordon model is shown to be equivalent to an SO(N )2 conformal field theory perturbed by a current-current interaction, w...

We study travelling kinks in the spatial discretizations of the nonlinear Klein–Gordon equation, which include the discrete φ lattice and the discrete sine–Gordon lattice. The differential advance-delay equation for travelling kinks is reduced to the normal form, a scalar fourth-order differential equation, near the quadruple zero eigenvalue. We show numerically non-existence of monotonic kinks...

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...

Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to derive, in a rigorous way, an effective nonlinear equation for the slowly varying field component in any order of the asymptotic procedure as expansions in the ...