TY - JOUR
T1 - A new plentiful solutions for nanosolitons of ionic (NSIW) waves spread the length of microtubules in (MLC) living cells
AU - Ouahid, Loubna
AU - Abdou, M. A.
AU - Al Shahrani, Jameelah S.
AU - Abdel-Baset, A. Mohamed
AU - Akgül, Ali
AU - Hassani, Murad Khan
N1 - Publisher Copyright:
© The Author(s) 2025.
PY - 2025/12
Y1 - 2025/12
N2 - This article describes the developed Paul-Painlike method (PPM) to provide striking ODE of the nanosoliton of the ionic waves (NSIW) that spread the length of microtubules in live cells. Furthermore, Auxiliary Equation Approach (AEA) and Sardar Sub Equation Approach (SSEA) have been utilized similarly and concurrently to determine solutions for this particular model. In providing a physical explanation, various solitary wave structures are visually represented. These solutions include the anti-kink, kink shape, singular kink wave shape, and periodic bright, bright-dark and dark-singular soliton solution. Additionally, graphical illustrations (both 2-D and 3-D) demonstrate how the various parameters utilized affect the validity of analytical results. Furthermore, the uniqueness of the solutions we derived is highlighted by comparing the differences with earlier solutions of the model. The solutions produced may be beneficial in a number of significant investigations in medicine, as well as biology. The results demonstrate the effectiveness of the proposed techniques for determining many optical solitons of nonlinear evolution equations.
AB - This article describes the developed Paul-Painlike method (PPM) to provide striking ODE of the nanosoliton of the ionic waves (NSIW) that spread the length of microtubules in live cells. Furthermore, Auxiliary Equation Approach (AEA) and Sardar Sub Equation Approach (SSEA) have been utilized similarly and concurrently to determine solutions for this particular model. In providing a physical explanation, various solitary wave structures are visually represented. These solutions include the anti-kink, kink shape, singular kink wave shape, and periodic bright, bright-dark and dark-singular soliton solution. Additionally, graphical illustrations (both 2-D and 3-D) demonstrate how the various parameters utilized affect the validity of analytical results. Furthermore, the uniqueness of the solutions we derived is highlighted by comparing the differences with earlier solutions of the model. The solutions produced may be beneficial in a number of significant investigations in medicine, as well as biology. The results demonstrate the effectiveness of the proposed techniques for determining many optical solitons of nonlinear evolution equations.
KW - Extended auxiliary equation approach (AEA)
KW - Paul-painleve method (PPM)
KW - Sardar sub equation approach (SSEA)
UR - http://www.scopus.com/inward/record.url?scp=85218675341&partnerID=8YFLogxK
U2 - 10.1038/s41598-024-83515-z
DO - 10.1038/s41598-024-83515-z
M3 - Article
C2 - 39979338
AN - SCOPUS:85218675341
SN - 2045-2322
VL - 15
JO - Scientific Reports
JF - Scientific Reports
IS - 1
M1 - 6190
ER -