Constructions of the soliton solutions to coupled nonlinear Schrödinger equation with advanced mathematical techniques
Source abstract
Abstract
In our research paper, we explore the application of mathematical techniques, both analytical and numerical, to solve the coupled nonlinear Schrödinger equation. To obtain accurate solutions, we use the improved, modified, extended tanh-function method. By breaking down the Schrödinger equation into real and imaginary components, we derive four interconnected equations. We analyze these equations using the generalized tanh method to find precise solutions. This set of equations is of great importance in quantum mechanics and helps us understand the behavior of quantum systems. We provide an analytical and numerical solution using the implicit finite difference. Our method is second-order in both space and time, and we have verified its stability through von Neumann’s stability analysis.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Nonlinear Photonic Systems · Nonlinear Waves and Solitons · Advanced Fiber Laser Technologies
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, College of Science, Taibah University , Al-Madinah Al-Munawarah, Saudi Arabia
References (42)
Show source-provided references
1. Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption10.1007/s00033-023-01976-0 ↗
2. Properties of solutions to porous medium problems with different sources and boundary conditions10.1007/s00033-019-1130-2 ↗
3. Application of new Kudryashov method to various nonlinear partial differential equations10.1007/s11082-022-04261-y ↗
4. On the dynamics of exact solutions to a (3 + 1)-dimensional YTSF equation emerging in shallow sea waves: Lie symmetry analysis and generalized Kudryashov method10.1016/j.rinp.2023.106432 ↗
5. New soliton wave solutions to a nonlinear equation arising in plasma physics10.32604/cmes.2023.027344 ↗
6. (g′/g)-expansion method to seek traveling wave solutions for some fractional nonlinear PDES arising in natural sciences10.31197/atnaa.1125691 ↗
7. New waves solutions of the (2 + 1)-dimensional generalized Hirota–Satsuma–Ito equation using a novel expansion method10.1016/j.rinp.2023.106450 ↗
8. New exact solutions of nontraveling wave and local excitation of dynamic behavior for GGKDV equation10.1016/j.rinp.2023.106463 ↗
9. Exact solitary wave and numerical solutions for geophysical KdV equation10.1016/j.jksus.2022.102087 ↗
10. Jacobian elliptic function method for nonlinear differential-difference equations10.1016/j.chaos.2005.04.071 ↗
11. Jacobian-elliptic-function and rogue-periodic-wave solutions of a high-order nonlinear Schrödinger equation in an inhomogeneous optical fiber10.1016/j.cjph.2022.11.023 ↗
12. A complex tanh-function method applied to nonlinear equations of Schrödinger type10.1016/j.chaos.2003.09.042 ↗
13. Traveling-wave and numerical solutions to a Novikov-Veselov system via the modified mathematical methods10.3934/math.2023062 ↗
14. Analytical and numerical investigation for Kadomtsev–Petviashvili equation arising in plasma physics10.1088/1402-4896/ab6ce4 ↗
15. Fundamental solutions for the coupled KdV system and its stability10.3390/sym12030429 ↗
16. Constructions of the travelling wave solutions to the MRLW equation and their stability and accuracy arising in plasma physics10.1007/s40819-023-01520-8 ↗
17. A study of traveling wave structures and numerical investigation of two-dimensional Riemann problems with their stability and accuracy10.32604/cmes.2022.018445 ↗
18. Exact and numerical solutions for the GBBM equation using an adaptive moving mesh method10.1016/j.aej.2021.03.023 ↗
19. Analytical and numerical investigations of the modified Camassa–Holm equation10.1007/s12043-021-02153-6 ↗
20. Structure of analytical and numerical wave solutions for the ito integro-differential equation arising in shallow water waves10.1016/j.jksus.2021.101375 ↗
21. New exact and numerical solutions for the KdV system arising in physical applications10.1080/25765299.2021.1899786 ↗
22. Construction of the numerical and analytical wave solutions of the Joseph–Egri dynamical equation for the long waves in nonlinear dispersive systems10.1142/s0217979220502896 ↗
23. Constructions of the soliton solutions to the good Boussinesq equation10.1186/s13662-020-03089-8 ↗
24. Constructions of solitary travelling wave solutions for ito integro-differential equation arising in plasma physics10.1016/j.rinp.2020.103533 ↗
25. Exact and numerical solitary wave structures to the variant Boussinesq system10.3390/sym12091473 ↗
26. Electromagnetic and Thomson effects during photothermal transport process of a rotator semiconductor medium under hydrostatic initial stress10.1016/j.rinp.2020.102983 ↗
27. The extended Jacobian elliptic function expansion approach to the generalized fifth order KdV equation
28. The new exact solutions for the deterministic and stochastic (2 + 1)-dimensional equations in natural sciences10.1080/16583655.2019.1644832 ↗
29. Numerical solutions of nonlinear parabolic equations with robin condition: Galerkin approach
30. On the L∞ convergence of a difference scheme for coupled nonlinear Schrödinger equations10.1016/j.camwa.2010.03.012 ↗
31. Numerical simulation of coupled nonlinear Schrödinger equation10.1016/s0378-4754(01)00324-x ↗
32. Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics10.1142/s0217979220502823 ↗
33. Comparison of third-order fractional partial differential equation based on the fractional operators using the explicit finite difference method10.1016/j.aej.2023.02.032 ↗
34. New approach on conventional solutions to nonlinear partial differential equations describing physical phenomena10.1016/j.rinp.2022.105936 ↗
35. Monge–ampére simulation of fourth order PDES in two dimensions with application to elastic–electrostatic contact problems10.1016/j.jcp.2017.08.032 ↗
36. Numerical solutions to two-dimensional fourth order parabolic thin film equations using the parabolic monge-ampere method10.3934/math.2023841 ↗
37. Moving mesh generation using the parabolic Monge–Ampère equation10.1137/080716773 ↗
38. Numerical investigation for the GRLW equation using parabolic monge ampere equation
39. A. R. Alharbi , “Numerical solution of thin-film flow equations using adaptive moving mesh methods,” Ph.D. thesis, Keele University, 2016.
40. An adaptive moving mesh method for thin film flow equations with surface tension10.1016/j.cam.2017.01.019 ↗
41. Solitary wave solutions to a fractional model using the improved modified extended tanh-function method10.3390/fractalfract7030252 ↗
42. Using Krylov methods in the solution of large-scale differential-algebraic systems10.1137/0915088 ↗