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 ℏ, which provides us with a simple way to adjust and control the convergence region of series solution.
Liao, S.J.: The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems. Ph.D. Thesis, Shanghai Jiao Tong University (1992)Google Scholar
Liao, S.J.: Beyond Perturbation: Introduction to the Homotopy Analysis Method. Chapman and Hall/CRC, Boca Raton, FL (2003)Google Scholar
Liao, S.J.: On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. J. Fluid Mech. 488, 189–212 (2003)Google Scholar
Liao, S.J.: A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Int. J. Heat Mass Transfer 48, 2529–2539 (2005)CrossRefzbMATHGoogle Scholar
Liao, S.J., Su, J., Chwang, A.T.: Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body. Int. J. Heat Mass Transfer 49, 2437–2445 (2006)CrossRefzbMATHGoogle Scholar
Liao, S.J., Magyari, E.: Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Z. Angew. Math. Phys. 57, 777–792 (2006)zbMATHCrossRefMathSciNetGoogle Scholar