论文信息 - LETTER TO THE EDITOR: Grammian N-soliton solutions of a coupled KdV system

LETTER TO THE EDITOR: Grammian N-soliton solutions of a coupled KdV system

From the Lax pair and the binary Darboux transformation of a coupled Korteweg-de Vries system, we show that its nonlinear superposition formula is identical to that obtained for the Kaup-Kupershmidt equation. Therefore, the N-soliton solution can be associated with a determinant of the Gram type.

C. Verhoeven | M. Musette

[1] Caroline Verhoeven,et al. Extended soliton solutions for the Kaup-Kupershmidt equation , 2001 .

[2] S. Sakovich,et al. Bäcklund transformation and special solutions for the Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations , 2001, nlin/0102001.

[3] Caroline Verhoeven,et al. Nonlinear superposition formula for the Kaup-Kupershmidt partial differential equation , 2000 .

[4] Robert Conte,et al. Bäcklund transformation of partial differential equations from the Painlevé–Gambier classification. I. Kaup–Kupershmidt equation , 1998 .

[5] O I Bogoyavlenskii,et al. Breaking solitons in 2+1-dimensional integrable equations , 1990 .

[6] S. Aranson,et al. The topological classification of cascades on closed two-dimensional manifolds , 1990 .

[7] Akira Nakamura,et al. A Bilinear N-Soliton Formula for the KP Equation , 1989 .

[8] M. Tabor,et al. The Painlevé property for partial differential equations , 1983 .

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

[10] B. Gambier,et al. Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes , 1910 .