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<p>The time-fractional (2 + 1)-dimensional Konopelchenko-Dubrovsky system serves as a crucial avenue for exploring nonlinear wave dynamics within the atmospheric realm, shedding light on intricate scattering effects and extended-range interactions pervasive in the tropical and mid-latitude troposphere. This equation plays a pivotal role in unraveling the complex interplay between equatorial and mid-latitude Rossby waves, providing invaluable insights into their interactions and dynamics, which are integral to understanding weather phenomena. Our study focuses on harnessing the power of the unified method and Sardar subequation method to dissect these waves, resulting in the derivation of numerous solutions that encapsulate the diverse wave patterns and behaviors inherent in the governed system. The novelty of this work lies in the application of advanced mathematical methods, such as the unified method and the Sardar sub-equation method. These methods not only provide a wide range of solutions including previously unreported phenomena. The unified method yields periodic, kink, singular, and dark wave solutions, while employing the Sardar subequation method unveils a spectrum of solutions encompassing kink, anti-kink, periodic, dark bright, and singular behaviors. The results can be applied to detect weather systems by analyzing wave patterns such as atmospheric and oceanic waves. Waves like Rossby waves, gravity waves, and Kelvin waves are often used in weather prediction, as they help identify changes in pressure, temperature, and wind patterns that influence weather forecasts. Additionally, we employ 3D and 2D graphical representations to visually convey the obtained solutions, further enhancing our understanding of nonlinear wave dynamics in atmospheric science. Our study not only helps us understand nonlinear wave dynamics in atmospheric science better but also shows how mathematical methods can explain complex natural phenomena in many areas of nonlinear science. We used the powerful features of Mathematica to do accurate calculations and create clear visualizations.</p>

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Dynamical behaviours of soliton solutions to the time-fractional (2+1)-dimensional Konopelchenko-Dubrovsky system by two powerful techniques

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Tayyaba Younas,
  • Jamshad Ahmad

摘要

The time-fractional (2 + 1)-dimensional Konopelchenko-Dubrovsky system serves as a crucial avenue for exploring nonlinear wave dynamics within the atmospheric realm, shedding light on intricate scattering effects and extended-range interactions pervasive in the tropical and mid-latitude troposphere. This equation plays a pivotal role in unraveling the complex interplay between equatorial and mid-latitude Rossby waves, providing invaluable insights into their interactions and dynamics, which are integral to understanding weather phenomena. Our study focuses on harnessing the power of the unified method and Sardar subequation method to dissect these waves, resulting in the derivation of numerous solutions that encapsulate the diverse wave patterns and behaviors inherent in the governed system. The novelty of this work lies in the application of advanced mathematical methods, such as the unified method and the Sardar sub-equation method. These methods not only provide a wide range of solutions including previously unreported phenomena. The unified method yields periodic, kink, singular, and dark wave solutions, while employing the Sardar subequation method unveils a spectrum of solutions encompassing kink, anti-kink, periodic, dark bright, and singular behaviors. The results can be applied to detect weather systems by analyzing wave patterns such as atmospheric and oceanic waves. Waves like Rossby waves, gravity waves, and Kelvin waves are often used in weather prediction, as they help identify changes in pressure, temperature, and wind patterns that influence weather forecasts. Additionally, we employ 3D and 2D graphical representations to visually convey the obtained solutions, further enhancing our understanding of nonlinear wave dynamics in atmospheric science. Our study not only helps us understand nonlinear wave dynamics in atmospheric science better but also shows how mathematical methods can explain complex natural phenomena in many areas of nonlinear science. We used the powerful features of Mathematica to do accurate calculations and create clear visualizations.