Approximate analytic solution GENERATION LONG SOLITARY WAVES homotopy analysis method Analytic technique Approximated solutions Bottom topography Critical flow EXPONENTIALLY STRETCHING SHEET Exact solution FLAT-PLATE FREE OSCILLATIONS H-curve HAM solutions HOMOTOPY ANALYSIS METHOD Heat and mass transfer Homotopy analysis methods KDV EQUATION KdV equation Korteweg-de Vries MAGNETIC-FIELD MHD NANOFLUIDS New homotopy analysis method Physics RADIATION SOLITONS System of first order differential equation TRANSCRITICAL FLOW