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