An estimate of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two ...An estimate of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two quaternion matrices which form an assortive pair. As applications, some known results are obtained as corollaries and a question in the matrix determinant theory is answered completely.展开更多
Based on the double determinant theory the problem about the determinant of Vandermonde's type over quaternion field is studied, and a necessary and sufficient condition that this double determinant is not equal t...Based on the double determinant theory the problem about the determinant of Vandermonde's type over quaternion field is studied, and a necessary and sufficient condition that this double determinant is not equal to zero is got.展开更多
Soliton solutions, rational solutions, Matveev solutions, complexitons and interaction solutions of the AKNS equation are derived through a matrix method for constructing double Wronskian entries. The latter three sol...Soliton solutions, rational solutions, Matveev solutions, complexitons and interaction solutions of the AKNS equation are derived through a matrix method for constructing double Wronskian entries. The latter three solutions are novel. Moreover, rational solutions of the nonlinear Schr?dinger equation are obtained by reduction.展开更多
基金supported in part by NCET (NCET06-9-23)NUDT (JC08-02-03)
文摘An estimate of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two quaternion matrices which form an assortive pair. As applications, some known results are obtained as corollaries and a question in the matrix determinant theory is answered completely.
文摘Based on the double determinant theory the problem about the determinant of Vandermonde's type over quaternion field is studied, and a necessary and sufficient condition that this double determinant is not equal to zero is got.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10371070, 10671121)
文摘Soliton solutions, rational solutions, Matveev solutions, complexitons and interaction solutions of the AKNS equation are derived through a matrix method for constructing double Wronskian entries. The latter three solutions are novel. Moreover, rational solutions of the nonlinear Schr?dinger equation are obtained by reduction.
