Sentence examples for determinant solution from inspiring English sources

Note that this formula is obtained from the gram type determinant solution of the coupled SP equation in Appendix.

In what follows, we derive the generalized double Wronskian determinant solution of system (2) by applying the Wronskian technique.

Therefore, equations (8), (33), (36 - 37) constitute the modified two-dimensional Toda lattice with self-consistent sources, and it possesses the Grammian determinant solution (28 - 29 28 - 29(34 - 35 34 - 35

In this paper, using the Hirota bilinear method and Chen's method, we discuss multiple-soliton solutions and a generalized double Wronskian determinant solution to system (2), respectively.

It is interesting for us to construct the two-dimensional Toda lattice equation with self-consistent sources having a generalized Casorati determinant solution via the source generation procedure.

In Section 2, we derived that the modified two-dimensional Toda lattice with self-consistent sources (8), (33), (36 - 37 36 - 37s the Grammian determinant solution (25), (26), (34), (35).

Recently, generalized Wronskian (Casorati) determinant solutions are constructed for continuous and discrete soliton equations [33 39].

Hence we think that these solutions may be the same as Casorati determinant solutions in essence, they may be different only in form, of course, the relation between two kinds of determinant solutions is worthwhile to be studied further.

The resulting set of eigenfunctions leads to complexitons through the Casoratian formulation, a feasible way has been presented to construct a broad class of Casorati determinant solutions including complexitons and generalized Casorati determinant solutions of the Toda lattice equation.

Besides soliton solutions, a broader class of solutions such as rational solutions, negatons, positons and complexitons solutions are obtained from the generalized Wronskian (Casorati) determinant solutions [33 38].

We show that the modified two-dimensional Toda lattice with self-consistent sources (8), (33), (36 - 37 36 - 37solved into the determinare identities by presolvedg intoGrammian and Casorathedeterminant solutidentities