Extended soliton solutions for the Kaup-Kupershmidt equation

We extend the N-soliton solutions of the Kaup-Kupershmidt equation on a nonzero background decreasing as (x + 1/a)-2. These new solutions describe the interaction of N solitary waves with a static bell-shaped wave. We give the conditions so that the Backlund transformation relating those solutions and the N-solitons of the Sawada-Kotera equation will be satisfied.

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

[2]  Allan P. Fordy,et al.  Some remarkable nonlinear transformations , 1980 .

[3]  Ignace Loris,et al.  On reduced CKP equations , 1999 .

[4]  Willy Hereman,et al.  Symbolic methods to construct exact solutions of nonlinear partial differential equations , 1997 .

[5]  David J. Kaup,et al.  A Bäcklund Transformation for a Higher Order Korteweg-De Vries Equation , 1977 .

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

[7]  R. Hirota.  Direct Methods in Soliton Theory (非線形現象の取扱いとその物理的課題に関する研究会報告) , 1976 .

[8]  A. Parker,et al.  On soliton solutions of the Kaup-Kupershmidt equation. II. “Anomalous” N -soliton solutions , 2000 .

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

[10]  A. Hone.  Non-autonomous He´non-Heiles systems , 1997, solv-int/9703005.

[11]  David J. Kaup,et al.  On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψxxx + 6Qψx + 6Rψ = λψ , 1980 .

[12]  D. Levi,et al.  Non-isospectral deformations and Darboux transformations for the third-order spectral problem , 1988 .

[13]  Xing-Biao Hu,et al.  Soliton solutions and symmetries of the 2+1 dimensional Kaup–Kupershmidt equation , 1999 .

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

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

[16]  A. Parker,et al.  On soliton solutions of the Kaup-Kupershmidt equation. I. Direct bilinearisation and solitary wave , 2000 .

[17]  Allan P. Fordy,et al.  The He´non-Heiles system revisited , 1991 .