Solitary wave effects of Woods-Saxon potential in Schrödinger equation with 3d cubic nonlinearity. (English) Zbl 1541.35416
Summary: In this research article, we apply the generalized projective Riccati equation method to construct traveling wave solutions of the 3d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential. The generalized projective Riccati equation method is a powerful and effective mathematical tool for obtaining exact solutions of nonlinear partial differential equations, and it allows us to derive a variety of traveling wave solutions of the 3d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential. These solutions contain periodic wave solutions, bright and dark soliton solutions. The study of many physical systems, such as Bose-Einstein condensates and nonlinear optics, that give rise to the nonlinear Schrödinger equation. We provide a detailed description of the generalized projective Riccati equation method in the paper, and demonstrate its usefulness in solving the nonlinear Schrödinger equation with Woods-Saxon potential. We present various graphical representations of the obtained solutions using MATLAB software, and analyze their characteristics. Our results provide new insights into the behavior of the 3d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential, and have potential applications in numerous fields of physics, as well as nonlinear optics and condensed matter physics.
Keywords:
3d cubic focusing nonlinear Schrödinger equation; Woods-Saxon potential; traveling wave solution; generalized projective Riccati equation method (GPREM)Software:
MatlabReferences:
| [1] | Onyenegecha C.P., Njoku I.J., Opara A.I., Echendu O.K., Omoko E.N., Eze F.C., Nwaneho F.U., “Nonrelativistic Solutions of Schrodinger Equation and Thermodynamic Properties with the Proposed Modified Mobius Square Plus Eckart Potential”, Heliyon, 8:2 (2022), e08952, 10 pp. · doi:10.1016/j.heliyon.2022.e08952 |
| [2] | Wei Gao-Feng, Long Chao-Yun, Duan Xiao-Yong, Dong Shi-Hai, “Arbitrary L-Wave Scattering State Solutions of the Schrodinger Equation for the Eckart Potential”, Physica Scripta, 77:3 (2008), 035001, 5 pp. · Zbl 1138.81530 · doi:10.1088/0031-8949/77/03/035001 |
| [3] | Morrison C.L., Shizgal B., “Pseudospectral Solution of the Schrodinger Equation for the Rosen-Morse and Eckart Potentials”, Journal of Mathematical Chemistry, 57:12 (2019), 1035-1052 · Zbl 1414.81093 · doi:10.1007/s10910-019-01007-2 |
| [4] | Onate C.A., Akanbi T.A., “Solutions of the Schrodinger Equation with Improved Rosen Morse Potential for Nitrogen Molecule and Sodium Dimer”, Results in Physics, 22:6 (2021), 103961, 7 pp. · doi:10.1016/j.rinp.2021.103961 |
| [5] | Desai A.M., Mesquita N., Fernandes V., “A New Modified Morse Potential Energy Function for Diatomic Molecules”, Physica Scripta, 95:8 (2020), 085401, 6 pp. · doi:10.1088/1402-4896/ab9bdc |
| [6] | Udoh M.E., Okorie U.S., Ngwueke M.I., Ituen E.E., Ikot A.N., “Rotation-Vibrational Energies for Some Diatomic Molecules with Improved Rosen-Morse Potential in D-Dimensions”, Journal of Molecular Modeling, 25:6 (2019), 1-7 · doi:10.1007/s00894-019-4040-5 |
| [7] | Carbo-Dorca R., Nath D., “Average Energy and Quantum Similarity of a Time Dependent Quantum System Subject to Poschl-Teller Potential”, Journal of Mathematical Chemistry, 60:2 (2022), 1-21 · Zbl 1487.81078 · doi:10.1007/s10910-021-01318-3 |
| [8] | Pereira L.C., Marangoni B.S., do Nascimento V.A., “Dynamics and Stability of Matter-Wave Solitons in Cigar-Shaped Bose-Einstein Condensates Dragged by Poschl-Teller Potential”, International Journal of Quantum Chemistry, 121:11 (2021), e26634, 9 pp. · doi:10.1002/qua.26634 |
| [9] | Jaramillo B., Martinez-y-Romero R.P., Nunez-Yepez H.N., Salas-Brito A.L., “On the One-Dimensional Coulomb Problem”, Physics Letters A, 374:2 (2009), 150-153 · Zbl 1235.81064 · doi:10.1016/j.physleta.2009.10.073 |
| [10] | Inyang E.P., William E.S., Obu J.A., “Eigensolutions of the \(N\)-Dimensional Schrodinger Equation Interacting with Varshni-Hulthen Potential Model”, Revista Mexicana de Fisica, 67:2 (2021), 193-205 · doi:10.31349/RevMexFis.67.193 |
| [11] | Chen Lu, Lu Guozhen, Zhu Maochun, “Sharp Trudinger-Moser Inequality and Ground State Solutions to Quasi-Linear Schrodinger Equations with Degenerate Potentials in \(\mathbb{R}^n\)”, Advanced Nonlinear Studies, 21:4 (2021), 733-749 · Zbl 1479.35264 · doi:10.1515/ans-2021-2146 |
| [12] | Lorca S., Montenegro M., “Spike Solutions of a Nonlinear Schrodinger Equation with Degenerate Potential”, Journal of Mathematical Analysis and Applications, 295:1 (2004), 276-286 · Zbl 1051.35089 · doi:10.1016/j.jmaa.2004.03.044 |
| [13] | Wenbo Wang, Quanqing Li, “Existence and Concentration of Positive Ground States for Schrodinger-Poisson Equations with Competing Potential Functions”, Electronic Journal of Differential Equations, 2020:78 (2020), 1-19 · Zbl 1448.35174 |
| [14] | Yan Zhenya, Wen Zichao, Konotop V.V., “Solitons in a Nonlinear Schrodinger Equation with PT-Symmetric Potentials and Inhomogeneous Nonlinearity: Stability and Excitation of Nonlinear Mordinary Differential Equations”, Physical Review A, 92:2 (2015), 023821, 8 pp. · doi:10.1103/PhysRevA.92.023821 |
| [15] | Deng Yangbao, Deng Shuguang, Tan Chao, Xiong Cuixiu, Zhang Guangfu, Tian Ye, “Study on Propagation Characteristics of Temporal Soliton in Scarff II PT-Symmetric Potential Based on Intensity Moments”, Optics and Laser Technology, 79 (2016), 32-38 · doi:10.1016/j.optlastec.2015.11.003 |
| [16] | Znojil M., “Exact Solution for Morse Oscillator in PT-Symmetric Quantum Mechanics”, Physics Letters A, 264:2-3 (1999), 108-111 · Zbl 0949.81020 · doi:10.1016/S0375-9601(99)00805-1 |
| [17] | Bo Wen-Bo, Wang Ru-Ru, Fang, Yin, Wang, Yue-Yue, Dai Chao-Qing, “Prediction and Dynamical Evolution Of Multipole Soliton Families in Fractional Schrodinger Equation with the PT-Symmetric Potential and Saturable Nonlinearity”, Nonlinear Dynamics, 111:2 (2022), 1-12 · doi:10.1007/s11071-022-07884-8 |
| [18] | Midya B., Roychoudhury R., “Nonlinear Localized Mordinary Differential Equations in PT-Symmetric Rosen-Morse Potential Wells”, Physical Review A, 87:4 (2013), 045803, 5 pp. · doi:10.1103/PhysRevA.87.045803 |
| [19] | Inc M., Iqbal M.S., Baber M.Z., Qasim M., Iqbal Z., Tarar M.A., Ali A.H., “Exploring the Solitary Wave Solutions of Einstein”s Vacuum Field Equation in the Context of Ambitious Experiments and Space Missions”, Alexandria Engineering Journal, 82 (2023), 186-194 · doi:10.1016/j.aej.2023.09.071 |
| [20] | Rehman, S.U., Nawaz R., Zia F., Fewster-Young N., Ali A.H., “A Comparative Analysis of Noyes-Field Model for the Non-Linear Belousov-Zhabotinsky Reaction Using Two Reliable Techniques”, Alexandria Engineering Journal, 93 (2024), 259-279 · doi:10.1016/j.aej.2024.03.010 |
| [21] | Yongyi Gu, Baixin Chen, Feng Ye, Najva A., “Soliton Solutions of Nonlinear Schrodinger Equation with the Variable Coefficients under the Influence of Woods-Saxon Potential”, Results in Physics, 42 (2022), 105979 · doi:10.1016/j.rinp.2022.105979 |
| [22] | Zayed E.M.E., Alurrfi K.A.E., “The Generalized Projective Riccati Equations Method for Solving Nonlinear Evolution Equations in Mathematical Physics”, Abstract and Applied Analysis, 2014 (2014), 259190 · Zbl 1472.35344 · doi:10.1155/2014/259190 |
| [23] | Yao Shao-Wen, Akram G., Sadaf M., Zainab I., Rezazadeh H., Inc M., “Bright, Dark, Periodic and Kink Solitary Wave Solutions of Evolutionary Zoomeron Equation”, Results in Physics, 43 (2022), 106117 · doi:10.1016/j.rinp.2022.106117 |
| [24] | Younis M., Sulaiman T.A., Bilal M., Rehman S.U., Younas U., “Modulation Instability Analysis, Optical and Other Solutions to the Modified Nonlinear Schrodinger Equation”, Communications in Theoretical Physics, 72:6 (2020), 065001, 12 pp. · Zbl 1451.82022 · doi:10.1088/1572-9494/ab7ec8 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
