Qualitative analysis, optical soliton solutions, overlapping phenomena, and image encryption of a nonlinear model arising in mathematical physics
Mohammad Safi Ullah, Tarmizi Usman, Mahinur Akter, Md. Ruhul Amin
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Source: Crossref
Published: Jun 20, 2026
DOI: 10.1142/s0217984926501563
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In this paper, we apply the unified solver process and the [Formula: see text]-model expansion methodology to explore the dual-mode nonlinear Schrödinger (DMNLS) equation. Several travelling-wave solutions are obtained, including dark and bright solitons, singular solutions, periodic breather waves, single- and multiple-breather waves, and a comparison of two overlapping solutions. These outcomes are graphically illustrated to show the effects of various parameters on the soliton profiles. The phase-plane dynamics of the investigated model are constructed to analyze the qualitative behavior of the adopted nonlinear structure. The suggested nonlinear system is employed in an image-encryption application, where it disperses and jumbles image pixels to enhance security. The results obtained will serve as a significant milestone in the investigation of nonlinear phenomena in mathematical physics and engineering.
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