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首页> 外文期刊>Journal of Computational Methods in Sciences and Engineering >A nonlinear second-order evolution equation - classical and nonclassical symmetry analyses and their physical implications
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A nonlinear second-order evolution equation - classical and nonclassical symmetry analyses and their physical implications

机译：非线性二阶发展方程-古典和非古典对称分析及其物理意义

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摘要

The classical Lie group formalism as well as the nonclassical procedure is applied to study a nonlinear partial differential equation of the second order. It is important to stress that until now no symmetry calculation is available. Therefore it seems indispensable to apply this method yielding a deeper insight into the behaviour of the solution manifold. Firstly we determine the classical Lie point symmetries including algebraic properties. Similarity solutions in a most general form and nonlinear transformations are obtained. Also a statement relating to potential symmetries is performed. Then we show how the equation leads to approximate symmetries and we apply the method for the first time. Secondly some important hints relating to different algebraic solution techniques are given in order to construct further closed-form solutions. We finally show how this less-studied equation admits solitary and peakon classes of solutions of practical relevance.
机译：应用经典的李群形式主义和非经典的方法研究二阶非线性偏微分方程。需要强调的是，到目前为止，还没有对称计算可用。因此，应用此方法似乎必不可少，从而可以更深入地了解溶液歧管的行为。首先，我们确定经典的李点对称性，包括代数性质。获得了最通用形式的相似性解和非线性变换。还执行与潜在对称性有关的声明。然后，我们展示了方程如何导致近似对称，并首次应用了该方法。其次，给出了与不同代数求解技术有关的一些重要提示，以便构造更多的封闭形式的求解。最后，我们显示了这个研究较少的方程式如何接纳具有实际意义的解决方案的孤立类和峰值类。

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