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
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.
