Dynamical Study with Exact Travelling Waves with High Amplitude Solitons to Clannish Random Walker’s Parabolic Equation

• Sheikh Zain Majid ^[1] ; Muhammad Imran Asjad ^[1] ; Sachin Kumar ^[2] ; Taseer Muhammad ^[3]
  1. [1] University of Management and Technology

     University of Management and Technology

     Estados Unidos

     
  2. [2] University of Delhi

     University of Delhi

     India

     
  3. [3] King Khalid University

     King Khalid University

     Arabia Saudí

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
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  • This article presents a range of new exact travelling wave solutions for the nonlinear time-fractional Clannish Random Walker’s Parabolic equation, utilising trigonometric and hyperbolic functions in the context of the beta derivative. This approach enables the effective modelling of non-local and memory effects in wave propagation. The proposed analytical methods significantly enhance computational efficiency, reliability, and effectiveness, providing a diverse set of exact travelling wave solutions. Modified auxiliary equation and the generalised projective Riccati equation methods are employed to extract travelling solitary wave solutions with high amplitude, unique periodic, dark and bright solitons, high amplitude lump wave, breather wave, kink wave, and anti-kink with multiple lump wave profiles. Using the modern software Maple, graphs of solitary travelling wave solutions in three-dimensional, contour, and two-dimensional formats are presented, effectively demonstrating the parameters’ impact. To observe dynamic insight, this study presents sensitivity and chaotic analysis. This study helps to predict lump and high amplitude soliton, showing stable and sharp transitions often happen in fluid dynamics and fibre optics.