The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Mathematical Physics Pub Date : 2023-11-28 DOI:10.1155/2023/4132763
Wei Gao, Haci Mehmet Baskonus
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Abstract

In this manuscript, we focus on the application of recently developed analytical scheme, namely, the rational sine-Gordon expansion method (SGEM). Some new exact solutions of Riemann wave system and the nonlinear Gross−Pitaevskii equation (GPE) by using this method are extracted. This method is based on the general properties of the SGEM which uses the fundamental properties of trigonometric functions. Many novel analytical solutions such as dark, bright, mixed dark–bright, hyperbolic, and periodic wave solutions are successfully extracted. Physical meanings of solutions are simulated by the various figures in 2D and 3D along with the contour graphs. Strain conditions of the existence are also reported in detail. Finally, modulation instability analysis of the nonlinear GPE is studied in detail.
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具有合算符和Riemann波动方程的非线性Gross - Pitaevskii模型的调制不稳定性分析及解析解
在本文中,我们重点介绍了最近发展的解析格式的应用,即有理正弦戈登展开法(SGEM)。利用这种方法提取了Riemann波系统和非线性Gross - Pitaevskii方程的一些新的精确解。该方法是基于SGEM的一般性质,利用三角函数的基本性质。成功地提取了许多新的解析解,如暗、亮、混合暗-亮、双曲和周期波解。通过二维和三维的各种图形以及等高线图来模拟解的物理意义。并详细报道了存在的应变条件。最后,对非线性GPE的调制不稳定性进行了详细的分析。
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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