N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions [PDF]
Mathematics, 2021 In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given.
Yu-Shan Bai, Peng-Xiang Su, Wen-Xiu Ma
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Finite Difference Solution Methods for a System of the Nonlinear Schrödinger Equations [PDF]
Nonlinear Analysis, 2004 This paper investigates finite difference schemes for solving a system of the nonlinear Schrödinger (NLS) equations. Several types of schemes, including explicit, implicit, Hopscotch-type and Crank-Nicholson-type are defined.
A. Kurtinaitis, F. Ivanauskas
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Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2006 Addition of higher nonlinear terms to the well known integrable nonlinear Schrödinger (NLS) equations, keeping the same linear dispersion (LD) usually makes the system nonintegrable. We present a systematic method through a novel Eckhaus-Kundu hierarchy,
Anjan Kundu
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Spectral Curves for the Derivative Nonlinear Schrödinger Equations [PDF]
Symmetry, 2021 Currently, in nonlinear optics, models associated with various types of the nonlinear Schrödinger equation (scalar (NLS), vector (VNLS), derivative (DNLS)), as well as with higher and mixed equations from the corresponding hierarchies are usually studied.
A. O. Smirnov
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Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations [PDF]
Journal of evolution equations (Printed ed.), 2019 A nonlinear Schrödinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrödinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations.
Younghun Hong +3 more
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On Blow-Up and Explicit Soliton Solutions for Coupled Variable Coefficient Nonlinear Schrödinger Equations [PDF]
MathematicsThis work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schrödinger equations (NLS) system with variable coefficients.
José M. Escorcia, Erwin Suazo
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Strong convergence rate of splitting schemes for stochastic nonlinear Schrödinger equations [PDF]
Journal of Differential Equations, 2017 In this paper, we show that solutions of stochastic nonlinear Schrodinger (NLS) equations can be approximated by solutions of coupled splitting systems.
J. Cui +3 more
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On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2017 We consider the Cauchy problem for the nonlinear Schrodinger equations (NLS) with non-algebraic nonlinearities on the Euclidean space. In particular, we study the energy-critical NLS on \begin{document}$ \mathbb{R}^d $\end{document} , \begin{document}$ d
Tadahiro Oh +2 more
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Soliton cluster solutions of nonlinear Schrödinger equations with variable coefficients in Bessel lattice [PDF]
Results in PhysicsThe goal of this article is to obtain soliton cluster solutions of (2 + 1)-dimensional nonlinear variable coefficient Schrödinger equations through computerized symbolic computation.
Shaofu Wang
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Decay estimates for nonlinear Schrödinger equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2020 In this short note, we present some decay estimates for nonlinear solutions of 3d quintic and 3d cubic NLS (nonlinear Schrodinger equations).
Chenjie Fan, Zehua Zhao
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