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Singularity Structure Analysis and Abundant New Dromion-like Structures for the (2+1)-Dimensional Generalized Burgers Equation
並列摘要
The Painleve (P) singularity analysis method (the WTC method, due to Weiss, Tabor and Carnevale) is a powerful tool for proving the P-property of nonlinear partial differential equations and their Bäcklund transformations. In this paper, the singularity structure analysis is performed for the (2+1)-dimensional generalized Burgers equation, ut + uxy + uuy + uxa^(-1)x uy = 0, by using the WTC method; it is shown that the equation passes the Panilev'e test. Based on the P-analysis, a Bäcklund transformation is obtained, and then it is used to find many exact solutions including N-soliton-like solutions and new exact solutions. Some of these obtained solutions are used to prove that the variable uy(x; y; t), rather than the physical field u(x; y; t) in the (2+1)-dimensional generalized Burgers equation, admits abundant dromion-like solutions (exponentially localized solutions) such as point dromions, ring dromions, extended dromions, sharp dromions and oscillatory dromion solutions.
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- Kumam, P., & Katchang, P. (2012). A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings. Journal of Applied Mathematics, 2012(), 1394-1428-299. https://doi.org/10.1155/2012/414831
- Sunthrayuth, P., & Kumam, P. (2012). A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems. Abstract and Applied Analysis, 2012(), 149-187-210. https://doi.org/10.1155/2012/316276
- Hou, Z. Y., Zhu, H. Y., & Feng, C. H. (2013). Existence and Global Uniform Asymptotic Stability of Almost Periodic Solutions for Cellular Neural Networks with Discrete and Distributed Delays. Journal of Applied Mathematics, 2013(), 102-107-412. https://doi.org/10.1155/2013/516293
- Shenan, J. M. (2014). Preserving Properties of Subordination and Superordination of Analytic Functions Associated with a Fractional Differintegral Operator. Tamkang Journal of Mathematics, 45(1), 63-75. https://doi.org/10.5556/j.tkjm.45.2014.1332
- Chuayjan, W., & Thianwan, S. (2009). Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space. Abstract and Applied Analysis, 2009(), 708-729. https://doi.org/10.1155/2009/613524