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Fractal localized structures related to Jacobian elliptic functions in the higher-order Broer-Kaup system 下载免费PDF全文
This work reveals a novel phenomenon—that the localized coherent structures of a (2﹢1)﹣dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2﹢1)﹣dimensional higher-order Broer-Kaup system as a concrete example. Starting from a B?cklund transformation, we obtain a linear equation, and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions. 相似文献
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A general mapping approach and new travelling wave solutions to the general variable coefficient KdV equation 下载免费PDF全文
A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein-Gordon equation. 相似文献
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Exact projective solutions of generalized nonlinear Schrödinger system with variable parameters 下载免费PDF全文
A direct self-similarity mapping approach is successfully applied to a generalized nonlinear Schrödinger (NLS) system. Based on the known exact solutions of a self-similarity mapping equation, a few types of significant localized excitation with novel properties are obtained by selecting appropriate system parameters. The integrable constraint condition for the generalized NLS system derived naturally here is consistent with the known compatibility condition generated via the Painlev? analysis. 相似文献
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Periodic wave solutions and solitary wave solutions to a generalized (3+1)-dimensional Gross--Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homogeneous balance principle and a mapping approach. These exact solutions exist under certain conditions via imposing suitable constraints on the functions describing dispersion, nonlinearity, and potential. The dynamics of the derived solutions can be manipulated by prescribing specific time-modulated dispersions, nonlinearities, and potentials. The results show that the periodic waves and solitary waves with novel behaviors are similar to similaritons reported in other nonlinear systems. 相似文献
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Exact projective solutions of a generalized nonlinear Schrdinger system with variable parameters 下载免费PDF全文
A direct self-similarity mapping approach is successfully applied to a generalized nonlinear Schrdinger (NLS) system. Based on the known exact solutions of a self-similarity mapping equation, a few types of significant localized excitation with novel properties are obtained by selecting appropriate system parameters. The integrable constraint condition for the generalized NLS system derived naturally here is consistent with the known compatibility condition generated via Painlev analysis. 相似文献
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New exact excitations and soliton fission and fusion for the (2+1)-dimensional Broer-Kaup-Kupershmidt system 总被引:3,自引:0,他引:3 下载免费PDF全文
With the help of an extended mapping approach, a series of new types of exact excitations with two arbitrary functions of the (2 1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific soliton fission and fusion solutions of the higher-dimensional BKK system are also obtained. 相似文献
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