Dynamic Characteristics of the Closed Soliton Solution and Phase Analysis of the (3+1)-Dimensional Jimbo-Miwa Equation
DOI:
https://doi.org/10.18034/ei.v12i1.745Keywords:
New auxiliary equation approach, (3+1)-dimensional Jimbo Miwa model, Exact Solution, Travelling wave solutions (TWSs)Abstract
The main purpose of this paper is to investigate abundant exact traveling wave solutions (TWSs) of the (3+1)-dimensional Jimbo Miwa model utilizing the innovative auxiliary equation technique. By applying this powerful technique, the obtained solutions reveal and elucidate various types of waves, which are essential for comprehensive studies of complex phenomena such as ocean dynamics and other related scientific and engineering areas. The auxiliary equation method has proven successful in yielding new and analytical soliton solutions, including trigonometric functions, rational functions, hyperbolic functions, and exponential functions for the given model. The results of these solutions are represented using 3-D, contour, and combined 2-D graphs, offering a more detailed and insightful visual interpretation. In particular, the velocity effect becomes more comprehensible when analyzing the 2-D plots. This paper also includes further phase plane analysis of the model to examine the solutions' behavior and characteristics. The results of this investigation have been compared with other researchers' findings available in the literature. This technique proves highly effective for various nonlinear models in generating innovative soliton solutions, which are essential in applied science and engineering.
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Copyright (c) 2024 M. Asif; Harun-Or Roshid; M. M. Rahman; M. F. Karim; A. Paul; Mst. Shekha Khatun
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