Symbolic computation and abundant travelling wave solutions to KdV–mKdV equation

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• 作者：SYED TAHIR RAZA RIZVI ; KASHIF ALI ; ALI SARDAR ; MUHAMMAD YOUNIS ; AHMET BEKIR
• 关键词：Novel (G′/G) ; expansion method ; KdV–mKdV equation ; travelling wave solutions.
• 刊名：Pramana
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：88
• 期：1
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics, general; Astronomy, Observations and Techniques; Astrophysics and Astroparticles;
• 出版者：Springer India
• ISSN：0973-7111
• 卷排序：88

文摘

In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.