Lax representation and bi-Hamiltonian structure of nonlinear Qiao model
Lax representation and bi-Hamiltonian structure of nonlinear Qiao model
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DOI：
10.1142/s0217984921506144
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发表时间：
2022-03-10
影响因子：
1.9
通讯作者：
Khater, Mostafa M. A.
中科院分区：
文献类型：
--
作者：
Khater, Mostafa M. A.
本文探索了非线性 Qiao 模型的精确、稳定和新颖的孤子波解。该模型于 2007 年导出，具有宽松的表示形式和双哈密顿结构，是完全可积层次结构中的第二个正成员。采用众所周知的广义扩展 tanh 函数方法来构造新颖的孤子波解。所获得的解决方案的稳定性与哈密顿系统的特征一起进行了检查。此外，通过将所获得的解与采用变分迭代（VI）方法获得的模型半解析解进行比较来检查所获得的解的准确性。所获得的解析和半解析解通过一些不同的图表进行演示，以显示所研究模型的更多物理和动态行为。检查所使用的解析和半解析方案的性能，以显示其是否有效和强大。
This paper explores accurate, stable, and novel soliton wave solutions of the nonlinear Qiao model. This model, which was derived in 2007, possesses a Lax representation and bi-Hamiltonian structure, where it is a second positive member in the utterly integrable hierarchy. The well-known generalized extended tanh-function method is employed to construct novel soliton wave solutions. The stable property of the obtained solutions is examined along with the Hamiltonian system's characterizations. Furthermore, the accuracy of the obtained solutions is checked by comparing it with the model's semi-analytical solutions that have been obtained by employing the variational iteration (VI) method. The obtained analytical and semi-analytical solutions are demonstrated through some distinct graphs to show more physical and dynamical behavior of the investigated model. The used analytical and semi-analytical schemes' performance is checked to show if it is effective and powerful.