Mamun Abdulla-Al, Ananna Samsun Nahar, An Tianqing, Shahen Nur Hasan Mahmud, Asaduzzaman Md
Department of Mathematics, College of Science, Hohai University, Nanjing-210098, PR China.
School of Science and Engineering, AM's Research Academy, Dhaka, Bangladesh.
Heliyon. 2021 Aug 2;7(8):e07704. doi: 10.1016/j.heliyon.2021.e07704. eCollection 2021 Aug.
In this current study, we described a modified extended tanh-function (mETF) method to find the new and efficient exact travelling and solitary wave solutions to the modified Liouville equation and modified regularized long wave (mRLW) equation in water wave mechanics. Travelling wave transformation decreases the leading equation to traditional ordinary differential equations (ODEs). The standardized balance technique provides the instruction of the portended polynomial related result stimulated from the mETF method. The substitution of this result follows the preceding step. Balancing the coefficients of the like powers of the portended solution leads to a system of algebraic equations (SAE). The solution of that SAE for coefficients provides the essential connection between the coefficients and the parameters to build the exact solution. Here the acquired solutions are hyperbolic, rational, and trigonometric function solutions. Our mentioned method is straightforward, succinct, efficient, and powerful and can be emphasized to establish the new exact solutions of different types of nonlinear conformable fractional equations in engineering and further nonlinear treatments.
在本研究中，我们描述了一种改进的扩展双曲正切函数（mETF）方法，以找到水波力学中修正的刘维尔方程和修正的正则化长波（mRLW）方程的新的、高效的精确行波和孤立波解。行波变换将主导方程简化为传统的常微分方程（ODE）。标准化平衡技术为mETF方法激发的预示多项式相关结果提供了指导。该结果的代入遵循前一步骤。平衡预示解的同次幂系数会导致一个代数方程组（SAE）。该SAE系数的解提供了系数与构建精确解的参数之间的基本联系。这里获得的解是双曲函数、有理函数和三角函数解。我们提到的方法直接、简洁、高效且强大，可用于建立工程中不同类型非线性共形分数方程的新精确解以及进一步的非线性处理。
