As a torqued version of the lattice potential Korteweg–de Vries equation, the H1^(a) is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme ...As a torqued version of the lattice potential Korteweg–de Vries equation, the H1^(a) is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme for this equation. Soliton solutions, Jordan-block solutions and soliton-Jordan-block mixed solutions are constructed by solving the determining equation set. All the obtained solutions have jumping property between constant values for fixed n and demonstrate periodic structure.展开更多
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
The problem of steady rotation of a composite sphere located at the centre of a spherical container has been investigated. A composite particle referred to in this paper is a spherical solid core covered with a permea...The problem of steady rotation of a composite sphere located at the centre of a spherical container has been investigated. A composite particle referred to in this paper is a spherical solid core covered with a permeable spherical shell. The Brinkman＇s model for the flow inside the compos- ite sphere and the Stokes equation for the flow in the spheri- cal container were used to study the motion. The torque ex- perienced by the porous spherical particle in the presence of cavity is obtained. The wall correction factor is calculated. In the limiting cases, the analytical solution describing the torque for a porous sphere and for a solid sphere in an un- bounded medium are obtained from the present analysis.展开更多
基金supported by the National Natural Science Foundation of China (No. 12071432)Zhejiang Provincial Natural Science Foundation (No. LZ24A010007)。
文摘As a torqued version of the lattice potential Korteweg–de Vries equation, the H1^(a) is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme for this equation. Soliton solutions, Jordan-block solutions and soliton-Jordan-block mixed solutions are constructed by solving the determining equation set. All the obtained solutions have jumping property between constant values for fixed n and demonstrate periodic structure.
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.
文摘The problem of steady rotation of a composite sphere located at the centre of a spherical container has been investigated. A composite particle referred to in this paper is a spherical solid core covered with a permeable spherical shell. The Brinkman＇s model for the flow inside the compos- ite sphere and the Stokes equation for the flow in the spheri- cal container were used to study the motion. The torque ex- perienced by the porous spherical particle in the presence of cavity is obtained. The wall correction factor is calculated. In the limiting cases, the analytical solution describing the torque for a porous sphere and for a solid sphere in an un- bounded medium are obtained from the present analysis.
