Lumps and their interaction solutions of a (2+1)-dimensional generalized potential Kadomtsev-Petviashvili equation

A (2+1)-dimensional generalized potential Kadomtsev-Petviashvili (gpKP) equation which possesses a Hirota bilinear form is constructed. The lump waves are derived by using a positive quadratic function solution. By combining an exponential function with a quadratic function, an interaction solution between a lump and a one-kink soliton is obtained. Furthermore, an interaction solution between a lump and a two-kink soliton is presented by mixing two exponential functions with a quadratic function. This type of lump wave just appears to a line $k_2x+k_3y+k_4t+k_5 \sim 0$. We call this kind of lump wave is a special rogue wave. Some visual figures are depicted to explain the propagation phenomena of these interaction solutions.     

Superconvergent estimates of conforming finite element method for nonlinear time‐dependent Joule heating equations

In this article, we study the superconvergence analysis of conforming bilinear finite element method (FEM) for nonlinear Joule heating equations. Based on the rigorous estimates together with high accuracy analysis of this element, mean value technique and interpolation postprocessing approach, the superclose and superconvergent estimates about the related variables in H¹‐norm are derived for semidiscrete and a linearized backward Euler fully discrete schemes, which extends the results of optimal estimates obtained for conforming FEMs in the previous literature. At last, a numerical experiment is performed to verify the theoretical analysis.     

Stabilization of unbounded bilinear control systems in Hilbert space

We consider bilinear control systems of the form y^′(t)=Ay(t)+u(t)By(t) where A generates a strongly continuous semigroup of contraction (etA)_t?0 on an infinite-dimensional Hilbert space Y whose scalar product is denoted by 〈.,.〉. We suppose that this system is unbounded in the sense that the linear operator B is unbounded from the state Y into itself. Tacking into account eventual control saturation, we study the problem of stabilization by (possibly nonquadratic) feedback of the form u(t)=−f(〈By(t),y(t)〉). Applications to the heat equation is considered.     

Riemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations

In this paper, based on a multidimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct multiperiodic Riemann theta functions periodic wave solutions for nonlinear equations such as the Caudrey-Dodd-Gibbon-Sawada-Kotera equation and (2+1)-dimensional breaking soliton equation. Among these periodic waves, the one-periodic waves are well-known cnoidal waves, their surface pattern is one-dimensional, and often they are used as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional so that they have two independent spatial periods in two independent horizontal directions. A limiting procedure is presented to analyze in detail, asymptotic behavior of the multiperiodic waves and the relations between the periodic wave solutions and soliton solutions are rigorously established. This generalized Hirota-Riemann method can also be demonstrated on a class variety of nonlinear difference equations such as Toeplitz lattice equation.     

一种灵活的基于身份的签名方案

在基于身份的密钥提取过程中,使密钥生成器在私钥中嵌入随机数,从而使得密钥提取具有较好的灵活性,使得用户对一个身份可具备多个私钥,这无疑会增加密钥使用的安全性;基于这种新的密钥提取思路,给出一个基于身份的签名体制,新的密钥提取方式使得它具有更好的安全性和灵活性;新的基于身份的签名体制中具有最少对运算,因此,与类似的方案相比,其具备较好的计算效率;新签名体制的安全性依赖于k-合谋攻击问题(k-CAAP)的困难性,其在适应性选择消息和ID攻击下具备强不可伪造性,并且其安全性证明具有紧规约性.     

Maximal resolvable packings and minimal resolvable coverings of triples by quadruples

Determination of maximal resolvable packing number and minimal resolvable covering number is a fundamental problem in designs theory. In this article, we investigate the existence of maximal resolvable packings of triples by quadruples of order v (MRPQS(v)) and minimal resolvable coverings of triples by quadruples of order v (MRCQS(v)). We show that an MRPQS(v) (MRCQS(v)) with the number of blocks meeting the upper (lower) bound exists if and only if v≡0 (mod 4). As a byproduct, we also show that a uniformly resolvable Steiner system URS(3, {4, 6}, {r₄, r₆}, v) with r₆≤1 exists if and only if v≡0 (mod 4). All of these results are obtained by the approach of establishing a new existence result on RH(6²ⁿ) for all n≥2. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 209–223, 2010     

Multiple soliton solutions for the sixth-order Ramani equation and a coupled Ramani equation

In this work, the completely integrable sixth-order nonlinear Ramani equation and a coupled Ramani equation are studied. Multiple soliton solutions and multiple singular soliton solutions are formally derived for these two equations. The Hirota’s bilinear method is used to determine the two distinct structures of solutions. The resonance relations for the three cases are investigated.     

Two-periodic waves and asymptotic property for generalized 2D Toda lattice equation

In this paper, two-periodic wave solutions are constructed for the (2 + 1)-dimensional generalized Toda lattice equation by using Hirota bilinear method and Riemann theta function. At the same time, we analyze in details asymptotic properties of the two-periodic wave solutions and give their asymptotic relations between the periodic wave solutions and the soliton solutions.     

Asymptotic behavior of the periodic wave solution for the (3+1)-dimensional Kadomtsev-Petviashvili equation

In this paper, the one- and two-periodic wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation are presented by means of the Hirota’s bilinear method and the Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.     

Quantum double constructions for compact quantum group

For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the universal and reduced quantum double constructions in the correspondence C＊-algebraic settings, which generalize Drinfeld＇s quantum double construction and yield new C＊-algebraic compact quantum groups.