On New Similarity Solutions of the Boiti–Leon–Pempinelli System |
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基金项目: | Acknowledgments Authors would like to express their sincere thanks to the reviewers for their valuable comments and suggestions, which improved the article to be worthy. |
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摘 要: | In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations (ODEs). Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.
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关 键 词: | 相似解 系统 常微分方程 偏微分方程 Lie对称性 物理背景 变换方法 精确求解 |
收稿时间: | 2013-06-03 |
On New Similarity Solutions of the Boiti-Leon-Pempinelli System |
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Authors: | Mukesh Kumar Raj Kumar |
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Institution: | Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Uttar Pradesh 211004, India |
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Abstract: | In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differential equations with one variable less at each step and eventually to a system of ordinary differential equations (ODEs). Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions. |
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Keywords: | Boiti-Leon-Pempinelli system similarity transformation method Lie group theory soliton solutions |
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