TY - JOUR
T1 - Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative
AU - Riaz, Muhammad Bilal
AU - Rehman, Aziz Ur
AU - Martinovic, Jan
PY - 2024
DA - July
Y2 - 2024
DO - 10.51537/chaos.1414782
JF - Chaos Theory and Applications
JO - CHTA
PB - Akif AKGÜL
WT - DergiPark
SN - 2687-4539
SP - 180
EP - 191
VL - 6
IS - 3
LA - en
AB - In this academic investigation, an innovative mapping approach is applied to complex three coupled Maccari’s system to unveil novel soliton solutions. This is achieved through the utilization of M-Truncated fractional derivative with employing the new mapping method and computer algebraic syatem (CAS) such as Maple. The derived solutions in the form of hyperbolic and trigonometric functions. Our study elucidates a variety of soliton solutions such as periodic, singular, dark, kink, bright, dark-bright solitons solutions. To facilitate comprehension, with certain solutions being visually depicted through 2-dimensional, contour, 3-dimensional, and phase plots depicting bifurcation characteristics utilizing Maple software. Furthermore, the incorporation of M-Truncated derivative enables a more extensive exploration of solution patterns. Our study establishes a connection between computer science and soliton physics, emphasizing the pivotal role of soliton phenomena in advancing simulations and computational modeling. Analytical solutions are subsequently generated through the application of the new mapping method. Following this, a thorough examination of the dynamic nature of the equation is conducted from various perspectives. In essence, understanding the dynamic characteristics of systems is of great importance for predicting outcomes and advancing new technologies. This research significantly contributes to the convergence of theoretical mathematics and applied computer science, emphasizing the crucial role of solitons in scientific disciplines.
KW - Complex three coupled Maccari’s system
KW - A new mapping method; Soliton patterns
KW - Bifurcation; M-Truncated fractional derivative
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UR - https://doi.org/10.51537/chaos.1414782
L1 - https://dergipark.org.tr/en/download/article-file/3639839
ER -