Chaos, solitons and fractals in (2 + 1)-dimensional KdV system derived from a periodic wave solution |
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Authors: | Chun-Long Zheng Gui-Ping Cai Ji-Ye Qiang |
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Institution: | aCollege of Physics and Mathematics, Zhejiang Lishui University, Lishui, Zhejiang 323000, PR China bInstitute of Educational Science, Wenzhou University, Wenzhou 325035, PR China |
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Abstract: | With the help of an extended mapping method and a linear variable separation method, new types of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with two arbitrary functions for (2 + 1)-dimensional Korteweg–de Vries system (KdV) are derived. Usually, in terms of solitary wave solutions and rational function solutions, one can find some important localized excitations. However, based on the derived periodic wave solution in this paper, we find that some novel and significant localized coherent excitations such as dromions, peakons, stochastic fractal patterns, regular fractal patterns, chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications. |
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