AbstractA nonlinear solution of wave profile equation directly derived from stream function is submitted. In stead of expressing by trigonometric series to approach the real solution, implicit function is adopted. In the era of electronic computer, Such an expression wi11 be convenient for practical utilization. Equations in either deep water or in finite water depth are worked out. They are proved more reasonable in graphical shape of wave profile and consistent in the continuity of wave celerity in various depth in comparison with Stokes theory.
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