Browsing by Author "Khalaf, Tamer M."

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Exploring the wave’s structures to the nonlinear coupled system arising in surface geometry
    (Scientific Reports, 2025-04-04) Farooq, Khizar; Hussain, Ejaz ; Younas, Usman ; Mukalazi, Herbert ; Khalaf, Tamer M. ; Mutlib, Abdul ; Shah, Syed Asif Ali
    In the area of scientific inquiry, scientists are increasingly intrigued by the subtle dynamics of natural occurrences. Leveraging cutting-edge approaches and procedures, they attempt to decode these complexities with more accuracy and insight. An important tool in this effort is the use of partial differential equations (PDEs) to create models that correctly capture these events. The expanding capacity of 3D visualization plays a crucial role in boosting researchers’ knowledge and analysis of such occurrences. By applying PDEs, scientists are able to reveal the complicated patterns controlling physical processes and give greater insights into their behavior. A soliton is an isolated solitary wave that propagates over a material without wasting energy or altering its shape due to contact with other waves. Solitons are distinct from regular wave occurrences due to their strong localization and remarkable stability and endurance. Soliton plays a crucial role in several disciplines of study such as nonlinear optics1,2, mechanics3, plasma physics4, engineering5, hydrodynamics6, communication systems7, optical fiber8, biology9, fluid dynamics10,11. Nonlinear partial differential equations (NLPDEs) grow as exceptionally crucial assets in this scientific pursuit. NLPDEs provide sophisticated insights into a wide range of fields, including optics, acoustics, plasma dynamics, and condensed matter physics. They not only increase our comprehension of the researched events but also allow scientists to make precise estimates about their future proliferation. As a result, many academics have committed to analyzing diverse NLPDEs, seeking to expand their comprehension of the exhibited behavior in the examined natural occurrences. Recent assessments have involved inquiries into the Batman–Burger equation12,13, Schrodinger equation14–18, Date–Jimbo–Kashiwara–Miwa equation19–21, thin film ferroelectric material equation22–25, Benjamin–Bona–Mahony equation26–28, Boussinesq equation29 generalized Calogero-Bogoyavlenskii-schiff equation33,34, Buckmaster equation35, non-linear non classical Sobolev-type wave model36, and different other37–49. T he study of the single-wave solutions of NLPDEs is significant for giving better views and understanding of the underlying process and useful uses. Therefore, numerous researchers have created new ways to study these NLPDEs answers. Plenty of strong techniques such as,exp (−χ expansion method50, extend mapping method51, homotopy perturbation method52, Darboux transformation53, exp-function method54, generalized Kudryashov method55, extended trial equation method56, Hirota bilinear method57, extended jacobian method58, extended direct algebric method59, improved extended fan-sub equation method60, modified extended tanh method, Backlund transform method61, Novel (G′ G expansion method62, extended auxiliary equation mapping method63, extended simple equation method64 and many more methods65–71.