loading page

New and more dual-mode solitary wave solutions for the Kraenkel-Manna-Merle system incorporating fractal effects
  • +2
  • Nauman Raza,
  • Zara Hassan,
  • Asma Butt,
  • Riaz Rahman,
  • Abdel-Haleem Abdel-Aty
Nauman Raza
University of the Punjab

Corresponding Author:[email protected]

Author Profile
Zara Hassan
University of the Punjab
Author Profile
Asma Butt
Author Profile
Riaz Rahman
Quaid-i-Azam University
Author Profile
Abdel-Haleem Abdel-Aty
University of Bisha
Author Profile


This paper introduces the fractal Kraenkel-Manna-Merle (KMM) system, that explains nonlinear short wave propagation with zero conductivity for saturated ferromagnetic materials in an external field. The semi inverse technique and the new auxiliary equation method (NAEM) are used to generate a new set of solutions. The proposed methods are more straightforward, succinct, accurate, and simple to calculate dual mode solitary wave solutions. A collection of exact soliton solutions specifically bright, dark, singular-shaped and singular-periodic are generated. The estimated solutions are obtained using constraint conditions and are displayed through 2D, 3D and contour plots with appropriate parametric values. The arbitrary functions in the solutions are chosen as unique functions to generate some novel soliton structures.
22 May 2021Submitted to Mathematical Methods in the Applied Sciences
23 May 2021Submission Checks Completed
23 May 2021Assigned to Editor
28 May 2021Reviewer(s) Assigned
03 Sep 2021Review(s) Completed, Editorial Evaluation Pending
04 Sep 2021Editorial Decision: Revise Minor
26 Sep 20211st Revision Received
27 Sep 2021Submission Checks Completed
27 Sep 2021Assigned to Editor
27 Sep 2021Reviewer(s) Assigned
27 Sep 2021Review(s) Completed, Editorial Evaluation Pending
28 Sep 2021Editorial Decision: Accept
25 Nov 2021Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.7967