In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a ...In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.展开更多
The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infinitec...The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infiniteconservation laws of the GNNV equation are obtained directly,without too much trick like Hirota’s bilinear method.展开更多
Any linear code can be used to construct a linear secret sharing scheme.In this paper,it is shown how to decide optimal linear codes(i.e.,with the biggest information rate)realizing a given access structure over finit...Any linear code can be used to construct a linear secret sharing scheme.In this paper,it is shown how to decide optimal linear codes(i.e.,with the biggest information rate)realizing a given access structure over finite fields.It amounts to solving a system of quadratic equations constructed from the given access structure and the corresponding adversary structure.The system becomes a linear system for binary codes.An algorithm is also given for finding the adversary structure for any given access structure.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,61021004,10735030Shanghai Leading Academic Discipline Project under Grant No.B412Program for Changjiang Scholars and Innovative Research Team in University(IRT0734)
文摘In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10735030,11075055,61021004,90718041,Shanghai Leading Academic Discipline Project (No. B412)Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)
文摘The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infiniteconservation laws of the GNNV equation are obtained directly,without too much trick like Hirota’s bilinear method.
基金supported by the Foundation of National Natural Science of China under Grant No.11271003the National Science Foundation (USA) under Grant No.DMS-0302549+1 种基金Guangdong Provincial Natural Science Foundation(China)under Grant No.S2012010009950High Level Talents Project of Guangdong,and Scientific Research Project of Education Bureau in Guangzhou under Grant No.2012A004
文摘Any linear code can be used to construct a linear secret sharing scheme.In this paper,it is shown how to decide optimal linear codes(i.e.,with the biggest information rate)realizing a given access structure over finite fields.It amounts to solving a system of quadratic equations constructed from the given access structure and the corresponding adversary structure.The system becomes a linear system for binary codes.An algorithm is also given for finding the adversary structure for any given access structure.
