基于Navier-Bernoulli假设和Love假设的可压缩Murnaghan材料圆柱弹性杆中非线性色散波孤子
Solitons of nonlinear dispersive wave steered from Navier-Bernoulli hypothesis and Love's hypothesis in the cylindrical elastic rod with compressible Murnaghan's materials
摘要：
应用Navier-Bernoulli假设和\cite{5}中的Love关系，导出了圆柱弹性杆内的非线性色散波动方程。弹性杆假定由Murnaghan材料如Lam $\acute{e}$系数、泊松比和本构常数组成，这些材料在本质上是可压缩的。在本研究中，我们应用两种积分架构，即扩展的sine-Gordon方法和修正的指数函数方法来研究色散波，并解决了孤子及其分类。证明了利用平衡原理得到的线性方程解的个数的存在性。模拟并绘制了相关的二维和三维图形，以显示复杂的结构。
英文摘要：
The nonlinear dispersive wave equation inside the cylindrical elastic rod is derived by applying the Navier-Bernoulli hypothesis and Love's relation in \cite{5}. The elastic rod is assumed to be composed of the Murnaghan's materials such as Lam$\acute{e}$'s coefficient, Poisson ratio and constitutive constant which are compressible in nature. In this research paper we apply the two integral architectures namely extended sine-Gordon method and modified exponential function method to study the dispersive wave and solved for the solitons and their classifications. The existence of the number of solutions are proved with respect to the linear equation obtained by balancing principle. The related two and three dimensional graphs are simulated and drawn to show the complex structures.
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