Painlevé analysis for various nonlinear Schrödinger dynamical equations

2021 ◽  
pp. 2150038
Author(s):  
Ijaz Ali ◽  
Aly R. Seadawy ◽  
Syed Tahir Raza Rizvi ◽  
Muhammad Younis
Keyword(s):  
Inverse Scattering ◽  
Schrodinger Equation ◽  
Nonlinear Models ◽  
Complete Integrability ◽  
Painlevé Analysis ◽  
Branch Points ◽  
Painlevé Test ◽  
Dynamical Equations ◽  
Nonlinear Schrödinger ◽  
Painleve Analysis

In this paper, our objective is to analyze integrability of three famous nonlinear models, namely unstable nonlinear Schrödinger equation (UNLSE), modified UNLSE (MUNLSE) as well as (2+1)-dimensional cubic NLSE (CNLSE) by utilizing Painlevé test ([Formula: see text]-test). The non-appearance of some sort of singularities such as moveable branch points indicates a sound probability of complete integrability of the concerned NLSE. In case an NLSE passes the [Formula: see text]-test, the studied model can be solved by implementing inverse scattering transformation (IST).

Painlevé analysis of a nonlinear Schrödinger equation discussing dynamics of solitons in optical fiber

2020 ◽  
pp. 2150005
Author(s):  
Syed T. R. Rizvi ◽  
Aly R. Seadawy ◽  
Ijaz Ali ◽  
Muhammad Younis
Keyword(s):  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Complete Integrability ◽  
Branch Points ◽  
Painlevé Test ◽  
Nonlinear Schrödinger ◽  
New Form

In this paper, we investigated a new form of nonlinear Schrödinger equation (NLSE), namely the Biswas–Arshed model (BAM) for the analysis of complete integrability with the help of Painlevé test ([Formula: see text]-test). By applying this test, we analyze the singularity structure of the solutions of BAM, knowing the fact that the absence of specific sort of singularities like moveable branch points is a patent signal for the complete integrability of the discussed model. Passing the [Formula: see text]-test is a powerful indicator that the studied model is resolvable by means of inverse scattering transformation (IST).

Riemann–Hilbert approach and multi-soliton solutions of a variable-coefficient fifth-order nonlinear Schrödinger equation with N distinct arbitrary-order poles

2021 ◽  
pp. 2150194
Author(s):  
Zhi-Qiang Li ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang ◽  
Jin-Jie Yang
Keyword(s):  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Arbitrary Order ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Fifth Order

Based on inverse scattering transformation, a variable-coefficient fifth-order nonlinear Schrödinger equation is studied through the Riemann–Hilbert (RH) approach with zero boundary conditions at infinity, and its multi-soliton solutions with [Formula: see text] distinct arbitrary-order poles are successfully derived. By deriving the eigenfunction and scattering matrix, and revealing their properties, a RH problem (RHP) is constructed based on inverse scattering transformation. Via solving the RHP, the formulae of multi-soliton solutions are displayed when the reflection coefficient possesses [Formula: see text] distinct arbitrary-order poles. Finally, some appropriate parameters are selected to analyze the interaction of multi-soliton solutions graphically.

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