Optical wave structures and stability analysis of integrable Zhanbota equation

In this research, the integrable Zhanbota-IIA equation which plays an important role in nonlinear optical dynamics is analytically investigated. Based on the extended sinh-Gordon equation expansion method, its bright, dark, combined bright-dark, singular soliton, combined singular soliton and singular periodic solutions are constructed under some constraint conditions. In addition, by using the modified Jacobi elliptic function expansion method, the Jacobi elliptic function solutions and the other soliton solutions are derived. Further, the modulational instability is studied based on the standard linear stability analysis. The graphical interpretations of the obtained results are demonstrated graphically. To the best of our knowledge, this study represents a unique and significant contribution to investigating the integrable Zhanbota-IIA equation. In addition, the extracted soliton solutions open doors to understanding the nonlinear systems more deeply and connecting their potential across a range of scientific and technological domains.