Soliton solutions for the fifth-order KdV equation with the homotopy analysis method. (English) Zbl 1170.76317

Summary: An analytic technique, the homotopy analysis method (HAM), is applied to obtain the soliton solution of the fifth-order KdV equation. The homotopy analysis method (HAM) provides us with a new way to obtain series solutions of such problems. HAM contains the auxiliary parameter \(\hbar\), which provides us with a simple way to adjust and control the convergence region of series solution.


76B25 Solitary waves for incompressible inviscid fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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