论文信息 - Pfaffian Representation of Solutions to the Discrete BKP Hierarchy in Bilinear Form

Pfaffian Representation of Solutions to the Discrete BKP Hierarchy in Bilinear Form

A discrete BKP hierarchy in bilinear form is given. It is shown that the solutions of the bilinear forms are given in terms of pfaffians and the bilinear equations of a discrete BKP hierarchy are reduced to an identity of pfaffians. The N -soliton solution is explicitly constructed in terms of the pfaffian. As an example of nonlinear difference equations, a difference analogue of the Sawada-Kotera equation is given from the discrete BKP hierarchy.

R. Hirota | S. Tsujimoto

[1] R. Hirota,et al. Discrete 2N-wave interaction , 1994 .

[2] B. Grammaticos,et al. Integrable lattices and convergence acceleration algorithms , 1993 .

[3] Yasuhiro Ohta,et al. Casorati and Discrete Gram Type Determinant Representations of Solutions to the Discrete KP Hierarchy , 1993 .

[4] Satoshi Tsujimoto,et al. Difference Scheme of Soliton Equations , 1993 .

[5] J. C. Eilbeck,et al. Future Directions of Nonlinear Dynamics in PhysicaL and Biological Systems , 1993 .

[6] R. Hirota,et al. Hierarchies of Coupled Soliton Equations. I , 1991 .

[7] J. Nimmo. Hall-Littlewood symmetric functions and the BKP equation , 1990 .

[8] Ryogo Hirota,et al. Soliton solutions to the BKP equations. II: The integral equation , 1989 .

[9] Ryogo Hirota,et al. Soliton Solutions to the BKP Equations. I. the Pfaffian technique , 1989 .

[10] Masaki Kashiwara,et al. Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type , 1982 .

[11] T. Miwa. On Hirota's difference equations , 1982 .

[12] Masaki Kashiwara,et al. KP Hierarchies of Orthogonal and Symplectic Type–Transformation Groups for Soliton Equations VI– , 1981 .

[13] Ryogo Hirota,et al. Nonlinear Partial Difference Equations. : I. A Difference Analogue of the Korteweg-de Vries Equation , 1977 .

[14] S. Sawada,et al. A Method for Finding N-Soliton Solutions of the KdV and KdV-Like Equation , 1974 .