Novel exact soliton solutions and bifurcation analysis of extended (2+1)-dimensional nonlinear Schrödinger equation with third-order dispersion using analytical powerful technique

The aim of this paper is to investigate soliton solutions of the extended (2+1)-dimensional nonlinear Schrödinger equation incorporating third-order dispersion and nonlinearity, which models the propagation of ultra-short optical pulses in nonlinear dispersive media. By employing the modified extended direct algebraic method, we successfully derive a rich variety of exact solutions, including bright, dark, and singular solitons. Moreover, we obtain periodic, singular periodic, hyperbolic, exponential, and Jacobi elliptic function solutions, as well as doubly periodic solutions expressed in terms of Weierstrass elliptic functions. In addition, we perform a bifurcation analysis to examine the phase space dynamics and identify the stability characteristics of the system’s fixed points. To illustrate the physical behavior of the derived solitons, 2D and 3D graphical simulations are presented, showcasing their evolution over time.