论文信息 - A generalized Hirota–Satsuma coupled Korteweg–de Vries equation and Miura transformations

A generalized Hirota–Satsuma coupled Korteweg–de Vries equation and Miura transformations

Abstract By introducing a 4×4 matrix spectral problem with three potentials, we propose a new hierarchy of nonlinear evolution equations. A typical equation in the hierarchy is a generalization of the Hirota–Satsuma coupled Korteweg–de Vries equation. Also, it is shown that the hierarchy possesses the generalized Hamiltonian form. Further, a Miura transformation related to the typical equation and its reductions are derived, from which some new coupled modified Korteweg–de Vries equations are obtained.

[1] G. Wilson,et al. The affine lie algebra C(1)2 and an equation of Hirota and Satsuma , 1982 .

[2] R. Hirota,et al. Soliton solutions of a coupled Korteweg-de Vries equation , 1981 .

[3] X. Geng,et al. New finite-dimensional integrable systems and explicit solutions of Hirota–Satsuma coupled Kortweg–de Vries equation , 1997 .

[4] Ryogo Hirota,et al. A coupled KdV equation is one case of the four-reduction of the KP hierarchy , 1982 .

[5] Tu Gui-Zhang,et al. On Liouville integrability of zero-curvature equations and the Yang hierarchy , 1989 .

[6] Allan P. Fordy,et al. On the integrability of a system of coupled KdV equations , 1982 .

[7] Decio Levi,et al. A hierarchy of coupled Korteweg-de Vries equations , 1983 .

[8] M. Jimbo,et al. Solitons and Infinite Dimensional Lie Algebras , 1983 .

[9] A. Chowdhury,et al. On the complete solution of the Hirota-Satsuma system through the 'dressing' operator technique , 1984 .