Nucci based soliton structures and nonlinear dynamics of the (3+1) dimensional hyperbolic Schrödinger equation
Afifa Shahbaz, Muhammad Abbas, M. Higazy, Muhammad Zain Yousaf, Meltem Ogrenmis, Asnake Birhanu, Y. S. Hamed · 2026
Read Nucci based soliton structures and nonlinear dynamics of the (3+1) dimensional hyperbolic Schrödinger equation by Afifa Shahbaz, Muhammad Abbas, M. Higazy, Muhammad Zain Yousaf, Meltem Ogrenmis, Asnake Birhanu, Y. S. Hamed (2026) in the Tower of Babel, a free online library of public-domain works preserved in clean, searchable text. No sign-up. The full text is served as a plain-text file at a predictable URL, where text is present: https://antarctic-labs.com/tower-of-babel/pmc-13542238.txt.
Description
Afifa Shahbaz, Muhammad Abbas, Higazy, Muhammad Zain Yousaf, Meltem Ogrenmis, Asnake Birhanu, and Hamed wrote a 2026 paper on waves in a nonlinear equation used across physics. The third author's name appears in the head in shortened form. The equation, a hyperbolic Schrödinger model in three space dimensions plus time, describes how wave packets move in media like fluids and cold atomic gases.
Using a reduction method tied to Nucci, the team found exact solutions: bright and dark solitons, repeating waves, and M- and W-shaped forms. Graphs in two and three dimensions show their shapes and stability. A further analysis shows the system can split into steady, oscillating, or chaotic behavior depending on starting conditions. Such solutions give test cases for simulations of real wave systems.
Catalog record
| CREATOR | Afifa Shahbaz, Muhammad Abbas, M. Higazy, Muhammad Zain Yousaf, Meltem Ogrenmis, Asnake Birhanu, Y. S. Hamed |
|---|---|
| YEAR | 2026 |
| COLLECTION | PAPERS |
| FORMAT | TXT |
| FILE SIZE | 110 KB |
| VERSION | 1.0 |
| LICENSE | CC BY 4.0 |
| RIGHTS | CC BY |
| SOURCE | Europe PMC |