Discussions on localized structures based on equivalent solution with different forms of breaking soliton model

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• 作者：Bin Zhang ; Xue-Long Zhang ; Chao-Qing Dai
• 关键词：Localized structures ; Modified tanh ; function method ; Different ansätz ; Variable ; coefficient breaking soliton model
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：87
• 期：4
• 页码：2385-2393
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

Although the modified tanh-function method was proposed to construct variable separation solutions many years ago, two important issues have not been emphasized: (1) the equivalence of variable separation solutions with different expressions by means of the modified tanh-function method; and (2) the universality of lack of physical meanings for some localized structures constructed by variable separation solutions. In this paper, we construct eleven types of variable separation solutions for the variable-coefficient breaking soliton system by means of the modified tanh-function method with three different ansätz, that is, positive-power ansatz, radical sign combined ansatz, and positive and negative power-symmetric ansatz. However, all other solutions with different forms can be re-derived from one of these solutions by means of some re-definitions of p and q. Therefore, solutions with different forms obtained by different ansätz of the modified tanh-function method are essentially equivalent. From this perspective, different ansätz are not really effective to construct so-called new solutions. Moreover, we study some localized coherent structures such as dromion, peakon and compacton for all components of the same model. We find if there is no divergent phenomenon for the other component, these localized coherent structures such as dromion, peakon and compacton are physical, otherwise, these localized coherent structures lose their values in the real application. We hope that these results have potential values to deeply investigate exact solutions and the related localized structures of nonlinear models in physics, engineering and biophysics.