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On nonclassical symmetries, Painlevé analysis and singular, periodic and solitary wave solutions of generalized Hirota-Satsuma coupled KdV system
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2022-07-14 , DOI: 10.1016/j.cnsns.2022.106710
Manjeet , Rajesh Kumar Gupta

In this work, we investigate the generalized Hirota-Satsuma coupled KdV system which is materialized in the theory of shallow water waves. Nonclassical symmetries of governing system are derived using Bluman and Cole method. The obtained symmetries are in the form of Jacobi elliptic functions, which are more generalized than earlier obtained symmetries for the governing system. Some new singular, periodic and solitary wave solutions of the governing system are also derived by assuming the Jacobi elliptic function type solutions. The obtained exact solutions for the considered system are verified by graphical representation. The Painlevé property of the considered system is also checked with the help of Kruksal’s method and symbolic computational tool Maple which shows the integrable behaviour of the considered system.



中文翻译:

关于广义 Hirota-Satsuma 耦合 KdV 系统的非经典对称性、Painlevé 分析和奇异、周期和孤立波解

在这项工作中,我们研究了在浅水波理论中具体化的广义 Hirota-Satsuma 耦合 KdV 系统。使用 Bluman 和 Cole 方法推导出治理系统的非经典对称性。得到的对称性是 Jacobi 椭圆函数的形式,它比以前得到的控制系统的对称性更普遍。通过假设 Jacobi 椭圆函数型解,还推导出了一些新的控制系统的奇异、周期和孤立波解。通过图形表示验证所考虑系统的精确解。在 Kruksal 方法和符号计算工具 Maple 的帮助下,还检查了所考虑系统的 Painlevé 属性,该工具显示了所考虑系统的可积行为。

更新日期:2022-07-14
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