One of the earliest applications of modern integrable systems theory (or “soliton theory”) to differential geometry was the solution of the problem of finding all constant mean curvature (CMC) tori in R3 (and therefore, by taking the Gauss map, finding all non-conformal harmonic maps from a torus to S2). At its simplest level this proceeds from the recognition that the Gauss-Codazzi equations o...

Algebro-geometric Poisson brackets for real, finite-zone solutions of the Korteweg–de Vries (KdV) equation were studied in [1]. The transfer of this theory to the Toda lattice and the sinh-Gordon equation is more or less obvious. The complex part of the finite-zone theory for the nonlinear Schrödinger equation (NS) and the sine-Gordon equation (SG) is analogous to KdV, but conditions that solut...

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...

Mục tiêu nghiên cứu: Nghiên cứu một số yếu tố liên quan đến tình trạng suy dinh dưỡng của trẻ mắc bệnh tim bẩm sinh điều trị tại viện Hà Nội năm 2021. Phương pháp mô tả cắt ngang 105 nhi sinh. Kết quả Tình nhi: Bình thường 45,7%, 54,3%; Phân loại dưỡng: Suy cấp chiếm 15,2%, mạn 22,9% và tiến triển 16,2%; Liên giữa với giới tính p = 0,067; nhóm tuổi: 0,084; cân nặng khi sinh: 0,021; phân 0,047. ...

Let f ≥ Ke,w. The goal of the present article is to characterize completely composite, Noetherian subsets. We show that U ≤ א0. J. Einstein [11] improved upon the results of X. Borel by studying functions. In [5], the authors address the splitting of null monodromies under the additional assumption that U ′ (T ′′) ≥ sinh −1 (wY ′) √ 2 8 ± g−1 (−ẑ) = ⋃ h ( 2× σ, . . . , t̂−2 ) = { T i : exp (u− i...

The recurrence algorithm is given for the calculation of NUAH B-splines in the space Sn+1 = span{sinh t, cosh t, t , · · · , t, t, 1} (n ≥ 3). The case of NUAH B-spline bases of low order with multiple knot sequences is studied. The limiting cases of UAH Bsplines are recovered when shape parameters α′s → 0and + ∞. Then the corresponding NUAH B-spline curve is defined and its main properties suc...

In this paper we study, analytically and numerically, the existence and blow up of solutions to two dimensional boundary value problems of the form ∆uλ = 0 in Ω, ∂uλ/∂n = Duλ + λf(uλ) on ∂Ω. We place particular emphasis on f(u) = sinh(u) = e u−e−u 2 , in which case the nonlinear flux boundary condition is frequently associated with the names of Butler and Volmer.

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficents can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counter-terms. We a...

The spectrum of finite-difference two-magnon operator is investigated for quantum S=1/2 chain with variable range exchange of the form h(j − k) ∝ sinh −2 a(j − k). It is found that usual bound state appears for some values of the total pseudomomentum of two magnons as for the Heisenberg chain with nearest-neighbor spin interaction. Besides this state, a new type of bound state with oscillating ...

We consider the quantum sinh-Gordon model in this paper. Form factors in this model were calculated in [1]–[3]. We sum up all contributions of form factors and obtain a closed expression for a correlation function. This expression is a determinant of an integral operator. Similar determinant representations were proven to be useful not only in the theory of correlation functions [4]–[12], but a...