An auto-B?cklund transformation for the quad equation Q1_(1) is considered as a discrete equation,called H2^(a),which is a so called torqued version of H2.The equations H2^(a) and Q1_(1) compose a consistent cube,from...An auto-B?cklund transformation for the quad equation Q1_(1) is considered as a discrete equation,called H2^(a),which is a so called torqued version of H2.The equations H2^(a) and Q1_(1) compose a consistent cube,from which an auto-B?cklund transformation and a Lax pair for H2^(a) are obtained.More generally it is shown that auto-B?cklund transformations admit auto-Backlund transformations.Using the auto-Backlund transformation for H2^(a)we derive a seed solution and a one-soliton solution.From this solution it is seen that H2^(a) is a semi-autonomous lattice equation,as the spacing parameter q depends on m but it disappears from the plane wave factor.展开更多
By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution i...By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution in terms of Wronskian form is obtained and verified. In addition, it is shown that the （N - 1）- and N-solitonic solutions satisfy the auto-Backlund transformation through the Wronskian technique.展开更多
基金supported by a La Trobe University China studies seed-funding research grantthe NSF of China[Grant Numbers 11875040 and 11631007]。
文摘An auto-B?cklund transformation for the quad equation Q1_(1) is considered as a discrete equation,called H2^(a),which is a so called torqued version of H2.The equations H2^(a) and Q1_(1) compose a consistent cube,from which an auto-B?cklund transformation and a Lax pair for H2^(a) are obtained.More generally it is shown that auto-B?cklund transformations admit auto-Backlund transformations.Using the auto-Backlund transformation for H2^(a)we derive a seed solution and a one-soliton solution.From this solution it is seen that H2^(a) is a semi-autonomous lattice equation,as the spacing parameter q depends on m but it disappears from the plane wave factor.
基金supported by National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Key Project of the Ministry of Education under Grant No.106033+2 种基金the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,the National Basic Research Program of China(973 Program)under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024,the Ministry of Education
文摘By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution in terms of Wronskian form is obtained and verified. In addition, it is shown that the （N - 1）- and N-solitonic solutions satisfy the auto-Backlund transformation through the Wronskian technique.
