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In this paper, the seventh-order Kaup–Kupershmidt (KK) equation arising in fluids and plasmas is considered. The pseudopotentials of the equation are derived, based on the pseudopotentials, the Lax pair of the equation is get, which shows that the equation has the Lax integrability. It is a very important property in researching nonlinear evolution equations (NLEEs). By virtue of the symbolic computation, the equation is transformed into its bilinear form and soliton solutions of the equation are obtained.

Lax Pair, Hirota Bilinear Form and Soliton Solutions of the Seventh-Order Kaup-Kupershmidt Equation in Plasma Physics