A MODEL EQUATION AND ITS EXACT TWO DIMENSIONAL SOLITARY WAVE SOLUTIONS FOR WATER WAVE DYNAMICS

Using the method of multiple scales and considering the nearly two-dimensional modulation of the waves when the dimensionless surface-tension coefficient τ of fluid is close to 1/3, we proposed a new model equation which we call the higher-order KP equation for water wave dgnamics. The exact and explicit two dimensional solitary wave solutions are also given.