in this paper, based on sinh-cosh method and sinh-gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.these solutions include jacobi elliptic function solution, soliton solution,trigonometric function solution.

In this paper, based on sinh-cosh method and sinh-Gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.These solutions include Jacobi elliptic function solution, soliton solution,trigonometric function solution.

and Applied Analysis 3 (a, b), and let g󸀠(x) ̸ = 0 on (a, b). If f󸀠(x)/g󸀠(x) is increasing (decreasing) on (a, b), then so are f (x) − f (a) g (x) − g (a) , f (x) − f (b) g (x) − g (b) . (11) If f󸀠(x)/g󸀠(x) is strictly monotone, then the monotonicity in the conclusion is also strict. Lemma 6 (see [11, Lemma 1.1]). Suppose that the power series f(x) = ∑ ∞ n=0 a n x n and g(x) = ∑∞ n=0 b n x n hav...

This paper provides an asymptotic estimate for the expected number of AMevel crossings of a random hyperbolic polynomial gi cosh x + g2 cosh 2x + ■ ■ ■ + g„ cosh nx , where g¡ (j = 1, 2,..., n) are independent normally distributed random variables with mean zero, variance one and K is any constant independent of x . It is shown that the result for K = 0 remains valid as long as K = K„ = 0{s/n).

The infinite series Rp = P ∞ k=1 (2k − 1) −p x 2k−1 , 0 < 1 − x 1, p = 2 or 3 , and the related series C(x, b, 2) = ∞ X k=1 (2k − 1) −2 cosh(2k − 1)x/ cosh(2k − 1)b, 0 < 1 − x/b 1, S(x, b, 3) = ∞ X k=1 (2k − 1) −3 sinh(2k − 1)x/ cosh(2k − 1)b, are of interest in problems concerning contact between plates and unilateral supports. This article will reexamine a previously published result of Barat...

Thermography can be used for the assessment of joint involvement in inflammatory arthritis. Modem thermographic apparatus allows temperature to be measured to within 0-2°C. and simultaneously records the areas involved. It has been demonstrated that thermographic changes in skin temperature over areas of chronic inflammation properly reflect changes in other chemical and cellular processes in r...

In the euclidean plane, a regular curve can be defined through its intrinsic equation which relates its curvature k to the arc length s. Elastic plane curves were determined this way. If k(s) = 2α cosh(αs) , the curve is known by the name “la courbe des forçats”, introduced in 1729 by Giovanni Poleni in relation with the tractrix [9]. The above equation is yet meaningful on a surface if one int...

Based on the second-order moments definition, beam propagation factor of a new mathematical model Hollow higher-order Cosh-Gaussian (HhCG) beams is investigated. Analytical formula for M2-factor HhCG derived, which depends hollowness parameter l, order n, cosh part δ and waist ω0. The influences these parameters are illustrated with numerical examples. result provides more general characteristi...

In this paper, the (G′/G)-expansion method is applied to seek traveling wave solutions of the combined and the double combined sinh-cosh-Gordon equations. This traveling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. It is shown that the proposed method is direct, effective and more general. 2000 Mathematics Subject Classification: 35K01; 35J05.