ABSTRACT In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. MATHEMATICS SUBJECT CLASSIFICATION 35 K9...

We compute the spectrum of the trigonometric Sutherland spin model of BCN type in the presence of a constant magnetic field. Using Polychronakos’s freezing trick, we derive an exact formula for the partition function of its associated Haldane–Shastry spin chain.

In this paper we give error bound for quadrature rules of Gaussian type for trigonometric polynomials with respect to the weight function w(x) = 1+cosx, x ∈ (−π, π), for 2π-periodic integrand, analytic in a circular domain. Obtained theoretical bound is checked and illustrated on some numerical examples.

Some new positive trigonometric sums that sharpen Vietoris’s classical inequalities are presented. These sharp inequalities have remarkable applications in geometric function theory. In particular, we obtain information for the partial sums of certain analytic functions that correspond to starlike functions in the unit disk. We also survey some earlier results with additional remarks and comments.

We prove that L∞-norming sets for finite-dimensional multivariate function spaces on compact sets are stable under small perturbations. This implies stability of interpolation operator norms (Lebesgue constants), in spaces of algebraic and trigonometric polynomials. 2010 AMS subject classification: 41A10, 41A63, 42A15, 65D05.

1. INTRODUCTION. In his Almagest, Ptolemy inscribes triangles in a unit circle, a circle with diameter d = 1 (see [5], pp. 90–92). This way the length of each side (now chord) represents the value of the trigonometric function sine of the opposite angle. A similar geometric interpretation of the cosine function is possible. In Figure 1 we present Ptolemy's famous sketch, juxtaposed with a " dua...

The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions an...

In this paper we find sharp inequalities of Jackson-Stechkin type between the best approximations periodic differentiable functions by trigonometric polynomials and generalized moduli continuity m-th order in space L_2. The exact values various n-widths classes from L_2 defined modus $r$-th derivative function f are calculated.

This paper presents a new approach and methodology to solve the second-order one-dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual finite difference scheme is used to discretize the time derivative. The cubic trigonometric B-spline basis functions are utilized as an interpolating function...

Abstract. An optimal set of quadrature formulas with an odd number of nodes for trigonometric polynomials in Borges’ sense [Numer. Math. 67 (1994), 271–288], as well as trigonometric multiple orthogonal polynomials of semi-integer degree are defined and studied. The main properties of such a kind of orthogonality are proved. Also, an optimal set of quadrature rules is characterized by trigonome...