Remarks on chaotic and fractal patterns based on variable separation solutions of (2+1)-dimensional general KdV equation

Abstract We obtain eleven types of variable separation solutions for the ( 2 + 1 )-dimensional general KdV equation by means of the extended tanh-function method, modified tanh-function method and improved tanh-function method with radical sign combine form ansatz. However, solutions obtained by different methods are essentially same. Moreover, when we construct chaotic and fractal patterns for a special component based on variable separation solution, we must consider solution expression of the other component in order to avoid many divergent and un-physical structures.

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