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引用次数: 0
摘要
本文采用改进的[公式:见正文]方法研究了流体力学中重要的时空分数布尔格方程和具有保形导数的时空耦合布森斯克方程。该过程行之有效,并产生了孤子解。该方法在符号计算工具 Maple 中得到了成功和稳定的应用。解还包含一些图形。研究还提供了这些方程的许多新的精确解,这些解不同于之前用所提方法发现的解。研究结果为各种类型的非线性系统提供了具有洞察力的理由,从而丰富了知识体系。研究结果证明了所提方法作为数学工具的价值,以及使用符号计算程序执行这些任务所带来的简便性、可靠性和速度提升。值得注意的是,它适用于数学物理中的许多非线性演化问题。
A novel study of analytical solutions of some important nonlinear fractional differential equations in fluid dynamics
The space-time fractional Burger-like equation and the space-time coupled Boussinesq equation with conformable derivative, both of which are significant in fluid dynamics, are investigated in this work using the improved [Formula: see text] method. The process works effectively and produces soliton solutions. The method was successfully and consistently implemented with Maple, a symbolic computing tool. The solutions also contain a few of graphics. Numerous novel exact solutions to these equations, distinct from those found earlier with the proposed approach, have been provided. The study’s findings add to the body of knowledge by offering insightful justifications for various types of nonlinear systems. The results demonstrated the value of the proposed method as a mathematical tool and the ease, dependability, and speed increases that result from carrying out these tasks using a symbolic computing program. Notably, it applies to many nonlinear evolution problems in mathematical physics.
期刊介绍:
MPLB opens a channel for the fast circulation of important and useful research findings in Condensed Matter Physics, Statistical Physics, as well as Atomic, Molecular and Optical Physics. A strong emphasis is placed on topics of current interest, such as cold atoms and molecules, new topological materials and phases, and novel low-dimensional materials. The journal also contains a Brief Reviews section with the purpose of publishing short reports on the latest experimental findings and urgent new theoretical developments.