Soliton solutions to a reverse-time non-local nonlinear Schrödinger differential equation

Huang, Qiaofeng; Ruan, Chenzhi; Huang, Zishan; Huang, Jiaxing

doi:10.1007/s12043-022-02491-z

Cited by 5 publications

(3 citation statements)

References 44 publications

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“…In recent years, research on the investigation of numerical solutions to differential equations has attracted the attention of researchers worldwide [1][2][3][4][5][6]. The quantum theory in physics and quantum mechanics involved with submicroscopic events [7] are primarily based on the Schrodinger equation (SE).…”

Section: Back Ground and Preliminariesmentioning

confidence: 99%

Stability, convergence and error analysis of B-spline collocation with Crank–Nicolson method and finite element methods for numerical solution of Schrodinger equation arises in quantum mechanics

Jena,

Senapati

2023

Phys. Scr.

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In the present study, the complex valued Schrodinger equation (CVSE) is solved numerically by a nonic B-spline finite element method (FEM) in quantum mechanics. The approach employed is based on collocation of nonic B-splines over spatial finite elements so that we have continuity of the dependent variable and its first eight derivatives throughout the solution range. For time discretization Crank-Nicolson scheme of second order based on FEM are employed. The method

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Section: Back Ground and Preliminariesmentioning

confidence: 99%

Stability, convergence and error analysis of B-spline collocation with Crank–Nicolson method and finite element methods for numerical solution of Schrodinger equation arises in quantum mechanics

Jena,

Senapati

2023

Phys. Scr.

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“…Introduction. -One of the core problems in nonlinear science is to solve the nonlinear partial differential equations (NPDEs) [1][2][3]. However, most NPDEs are extremely complex, and it is often difficult to derive their solutions.…”

mentioning

confidence: 99%

“…Up to now, many different solutions have been obtained for eq. (1). In [28], the Pfaffian technique is used to find the Pfaffian solutions.…”

mentioning

confidence: 99%

Multi-soliton solutions and soliton molecules of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for the incompressible fluid

Wang,

Shi

2024

EPL

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The (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) is explored in this letter. The multi-soliton solutions (MSSs) are probed via the Hirota bilinear form that is extracted by taking advantage of the Cole-Hopf transform. The soliton molecules (SMs) on the different planes such as the (x,y)-,(x,t)- and (y,t)- planes are investigated via assigning the velocity resonance mechanisms to the MSSs. The dynamic characteristics of the results are also unveiled graphically to show the corresponding physical behaviors.

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Revisit of rogue wave solutions in the Yajima–Oikawa system

Huang²,

Zhang³

et al. 2023

Nonlinear Dyn

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Soliton solutions to a reverse-time non-local nonlinear Schrödinger differential equation

Cited by 5 publications

References 44 publications

Stability, convergence and error analysis of B-spline collocation with Crank–Nicolson method and finite element methods for numerical solution of Schrodinger equation arises in quantum mechanics

Stability, convergence and error analysis of B-spline collocation with Crank–Nicolson method and finite element methods for numerical solution of Schrodinger equation arises in quantum mechanics

Multi-soliton solutions and soliton molecules of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for the incompressible fluid

Revisit of rogue wave solutions in the Yajima–Oikawa system

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