Dynamical behaviours of the multi-solitons and rogue waves in the Aizhan-Gudekli-Nurshuak-Zhanbota model with the N-fold Darboux transformation in nonlinear sciences

Nonlinear integrable systems play a crucial role in many areas of science, such as fluid dynamics, applied mathematics, nonlinear optics, and plasma physics. These models are particularly valuable for studying wave propagation and interaction effects. In this work, we examine the (1+1)-dimensional Aizhan-Gudekli-Nurshuak-Zhanbota model ( AGNZM ), a new integrable model possessing significant nonlinear characteristics. Employing the N-fold Darboux Transformation ( DT ) method for the associated Lax pair (LP), we construct analytic multi-soliton solutions of the AGNZM . We also derive first and second order rogue wave solutions, emphasizing the equation’s ability to capture extreme localised wave phenomena. We support the analytical solutions with graphical presentations of their dynamical behaviour. This study enhances our understanding of nonlinear wave structures and contributes to the broader investigation of integrable systems in mathematical physics and computational modeling.