| 对称理论在解若干非线性问题中的应用 |
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| 引用本文： | 刘希忠. 对称理论在解若干非线性问题中的应用[J]. 宁波大学学报(理工版), 2020, 33(5): 77-82 |
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| 作者姓名： | 刘希忠 |
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| 作者单位： | 绍兴文理学院 数理信息学院, 浙江 绍兴 312000 |
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| 摘 要： | 将摄动理论和对称约化理论结合起来对研究扰动非线性方程具有重要的意义. 本文利用近似对称约化理论研究了扰动mKdV方程, 得到了该方程的各阶近似约化方程和级数约化解. 本文还讨论了同伦近似对称方法在求解不可积系统中的应用以及利用对称和守恒律的关系求解非线性系统的无穷多守恒律等问题.
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| 关 键 词： | 对称 摄动理论 近似约化解 守恒律 同伦近似对称 |
Application of symmetry theory in solving nonlinear problems |
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| LIU Xizhong. Application of symmetry theory in solving nonlinear problems[J]. Journal of Ningbo University(Natural Science and Engineering Edition), 2020, 33(5): 77-82 |
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| Authors: | LIU Xizhong |
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| Affiliation: | College of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China |
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| Abstract: | The approximate symmetry method, which combines perturbation theory and Lie symmetry approach, proves very effective in solving perturbed nonlinear systems. In this paper, we investigate the perturbed mKdV equation using the approximate symmetry method to obtain its symmetry reduction equations of different orders and series reduction solutions. Also, we discuss the role of approximate homotopy symmetry method in solving non-integrable systems and how to acquire infinitely many conservation laws using the relationship between symmetry and conservation laws. |
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| Keywords: | symmetry perturbation theory approximate reduction solution conservation law approximate homotopy method |
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