Adequate Closed Form Wave Solutions to the Generalized KdV Equation in Mathematical Physics  

作　　者：Md. Munnu Miah Md. Al Amin Meia Md. Matiur Rahman Sarker Ahammodullah Hasan Md. Munnu Miah;Md. Al Amin Meia;Md. Matiur Rahman Sarker;Ahammodullah Hasan(Department of Mathematics, Islamic University, Kushtia, Bangladesh;Department of Mathematics, Government Titumir College, Dhaka, Bangladesh;Department of Pharmacy, University of Asia Pacific, Dhaka, Bangladesh)

机构地区：[1]Department of Mathematics, Islamic University, Kushtia, Bangladesh [2]Department of Mathematics, Government Titumir College, Dhaka, Bangladesh [3]Department of Pharmacy, University of Asia Pacific, Dhaka, Bangladesh

出　　处：《Journal of Applied Mathematics and Physics》2024年第6期2069-2082,共14页应用数学与应用物理（英文）

摘　　要：In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.

关 键 词：The Generalized KdV Equation The exp(-τ(ξ)) -Expansion Method Travelling Wave Solitary Wave 

分 类 号：O17[理学—数学]