Series Solution of High Order Abel, Bernoulli, Chini and Riccati Equations

To help solving intractable nonlinear evolution equations (NLEEs) of waves in the field of fluid dynamics we develop an algorithm to find new high order solutions of the class of Abel, Bernoulli, Chini and Riccati equations of the form (Formula Presented), with constant coefficients a, b, c. The role of this class of equations in NLEEs is explained in the introduction below. The basic algorithm to compute the coefficients of the power series solutions of the class, emerged long ago and is further developed in this paper. Practical application for hitherto unknown solutions is exemplified.