Tarmizi Usman, Mohammad Safi Ullah, Evi Safitri, M. Zulfikar Ali
This article presents novel soliton solutions for the nonlinear Schrodinger € equation with cubic nonlinearity, which arises in quantum mechanics and nonlinear optics. The ordinary differential framework of this model is obtained using a traveling wave transformation. We employ the unified, improved Kudryashov, and generalized Kudryashov methods to derive exact analytical solutions. These include rational, hyperbolic, exponential, and trigonometric forms, yielding diverse soliton structures such as bright-dark breathers, multiple breathers, localized breathers, periodic waves, double-periodic waves, kinks, and antikinks. The physical behavior of these solutions is illustrated graphically. A Hamiltonian analysis is used to examine the energy conservation and the stability of the solution, and the stability of equilibrium points is studied under various parameters. Our results align with previous findings and may be useful in understanding nonlinear wave behavior in physics, engineering, and applied mathematics. Copyright © 2025 by ASME.
Department of Mathematics, Universitas Syiah Kuala, Banda Aceh, 23111, Indonesia; Department of Mathematics, Comilla University, Cumilla, 3506, Bangladesh; Graduate School of Mathematics and Applied Sciences, Universitas Syiah Kuala, Banda Aceh, 23111, Indonesia; Department of Mathematics, University of Rajshahi, Rajshahi, 6205, Bangladesh
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