Simplified Method and Improved Solution for Deriving Fifth Order Stokes Wave

As the solution of the two equations for determining the existing fifth order Stokes wave de-rived by Skjelbreia is complex and tedious,the two equations are simplified into one equation for deter-mining d/L,i.e.,f(H,T,d/L)=0.According to this simplified method,three cases of the solution forthe Skjelbreia equations have been found:one accurate solution;more than one accurate solution and noaccurate solution(but there exists the optimum approximate solution in the area of satisfying Skjelbreiaequations).As to the case of more than one accurate solution,the reasonable solution can be judged fromthe method of variational principle,by means of which an optimum solution improved from the solutionof Skjelbreia equations in the area of satisfying the original mathematical equations of non-vortex andnonlinear wave theory,i.e.,the optimum fifth order Stokes wave,is given.

Simplified Method and Improved Solution for Deriving Fifth Order Stokes Wave

As the solution of the two equations for determining the existing fifth order Stokes wave derived by Skjelbreia is complex and tedious, the two equations are simplified into one equation for determining d/ L, i. e., f(H, T, d / L) = 0. According to this simplified method, three cases of the solution for the Skjelbreia equations have been found: one accurate solution; more than one accurate solution and no accurate solution (but there exists the optimum approximate solution in the area of satisfying Skjelbreia equations). As to the case of more than one accurate solution, the reasonable solution can be judged from the method of variational principle, by means of which an optimum solution improved from the solution of Skjelbreia equations in the area of satisfying the original mathematical equations of non-vortex and nonlinear wave theory, i. e., the optimum fifth order Stokes wave, is given.