Simulation of new waves in applied sciences via Schrödinger equations

Abstract

The perturbed chiral nonlinear Schrö dinger equation (PCNLSE) reflects the quantum actions such as quantum pictures of Bohm potential and internal self-potential properties. Indeed, this equation introduces the basics of the hidden variable theory in quantum mechanics. Two unified solver methods and exp$(-\phi (\xi \left)\right)$-expansion technique applied to PCNLSE to present many solitonic solutions in an explicit and effective way. The behaviour of these solutions is of qualitatively different structural natures, relying on physical coefficient parameters. The application of three mathematical techniques to our model system provides us with several possible physical property solutions that account for the majority of many phenomena the model under study attempts to depict. The reported bright explosive envelopes, explosive solitons, periodic blow up, bright periodic envelope and huge solitary waves are highly applicable in plasma and nuclear physics, optical communications, electro-magnetic propagations, superfluid and in a lot other applied sciences. The results of this system's solitary structures are consistent with the characteristics of the nonlinear Schrödinger equation systems used to study dispersive modes and higher-order perturbed systems. For more details about the physical dynamical representation of the presented solutions, we have illustrated them with profile pictures using Mathematica and Matlab 18, to obtain complete configurations. The proposed approach can be applied to several equations arising in all applied sciences.

Keywords:

• Perturbative chiral NLSE
• solvers and exp$(-\phi (\xi \left)\right)$-expansion methods
• chiral solitonic structures
• physical applications
• Mathematica and Matlab

AMS subject classifications::

• 34A34
• 35A20
• 35C08
• 35Q51
• 35Q55
• 35Q80

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All the data are available within the article.

Additional information

Funding

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through [project number RI-44-0764].