Faster and Slower Soliton Phase Shift: Oceanic Waves Affected by Earth Rotation

Mostafa M A Khater,Aliaa Mahfooz Alabdali

doi:10.3390/math9243223

Mostafa M A Khater, Aliaa Mahfooz Alabdali

Open Access

https://doi.org/10.3390/math9243223

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Abstract

This research paper investigates the accuracy of a novel computational scheme (Khater II method) by applying this new technique to the fractional nonlinear Ostrovsky (FNO) equation. The accuracy of the obtained solutions was verified by employing the Adomian decomposition (AD) and El Kalla (EK) methods. The AD and EK methods are considered as two of the most accurate semi-analytical schemes. The FNO model is a modified version of the well-known Korteweg–de Vries (KdV) equation that considers the effects of rotational symmetry in space. However, in the KdV model, solutions to the KdV equations substitute this effect with radiating inertia gravity waves, and thus this impact is ignored. The analytical, semi-analytical, and accuracy between solutions are represented in some distinct plots. Additionally, the paper’s novelty and its contributions are demonstrated by comparing the obtained solutions with previously published results.

Highlights

Plasma physics is one of the most crucial fields of our time which is attracting a large number of researchers [1,2]
We studied the analytical solutions of the fractional nonlinear Ostrovsky (FNO) equation which is given by [35,36,37,38]
Applying the Adomian decomposition (AD) and El Kalla (EK) methods to the FNO model based on the obtained analytical solutions (8), (10) and (12) when α = −1, c = 3, δ = −4

Summary

Introduction

Plasma physics is one of the most crucial fields of our time which is attracting a large number of researchers [1,2]. Many fractional derivatives have been derived to convert the fractional nonlinear partial differential equations into ordinary differential equations with integer-order such as He’s fractional derivative and the two-scale fractal derivative [21,22,23] These models are used to describe a wide variety of complicated events in various disciplines, including biology, quantum physics, electrochemistry, mechanical engineering, and mechanical sciences [24,25,26,27,28]. Several researchers failed to examine and provide a cohesive strategy applicable to all NLPDEs [32,33,34] In this context, we studied the analytical solutions of the FNO equation which is given by [35,36,37,38].

Solutions’ Accuracy

Results and Discussion

Conclusions