Abstract
With the aid of an improved projective approach and a linearvariable separation method, new types of variable separationsolutions (including solitary wave solutions, periodic wavesolutions, and rational function solutions) with arbitraryfunctions for (2+1)-dimensional Korteweg-de Vries system arederived. Usually, in terms of solitary wave solutions and rationalfunction solutions, one can find some important localizedexcitations. However, based on the derived periodic wave solutionin this paper, we find that some novel and significant localizedcoherent excitations such as dromions, peakons, stochasticfractal patterns, regular fractal patterns, chaotic line solitonpatterns as well as chaotic patterns exist in the KdV system asconsidering appropriate boundary conditions and/or initial qualifications.
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