The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation

Details The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation

2001-08-15

arxiv.org/abs/nlin/0108026v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

In this paper, some notes of the homogeneous balance (HB) method are discussed by a kind of general fifth-order KdV (fKdV) equation. Frist, the auto-B\"acklund transformation and lax represents of the higher-order KdV equation(a specific forms of fKdV equation) are obtained by the HB method. Then, the connection of the Hirota transformation and the HB method is discussed by two specific fKdV equations: the Sawada-Kotera equation and the Lax's equation. At the same time, the solitary wave solution of the general fifth-order KdV equation is obtained.

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