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Regularity properties of the cubic biharmonic Schrödinger equation on the half line
In this paper we study the regularity properties of the cubic biharmonic Schrödinger equation posed on the right half line. We prove local...
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Convergence Analysis of the Localized Orthogonal Decomposition Method for the Semiclassical Schrödinger Equations with Multiscale Potentials
We provide a convergence analysis of the localized orthogonal decomposition (LOD) method for Schrödinger equations with general multiscale potentials...
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Exponential decay estimates for fundamental matrices of generalized Schrödinger systems
In this article, we investigate systems of generalized Schrödinger operators and their fundamental matrices. More specifically, we establish the...
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Solvability in the sense of sequences for some logarithmic Schrödinger operators in higher dimensions
We study the solvability of certain linear nonhomogeneous equations containing the logarithm of the sum of the two Schrödinger operators in higher...
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A radial basis function-Hermite finite difference (RBF-HFD) method for the cubic-quintic complex Ginzburg–Landau equation
In this paper, the cubic–quintic complex Ginzburg–Landau (CQCGL) equation is numerically studied in 1D, 2D and 3D spaces. First, by the Strang...
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Existence and Stability of Standing Waves for the Mixed Dispersion Nonlinear Schrödinger Equation with a Partial Confinement in \({\mathbb {R}}^{N}\)
In this paper, we are devoted to the existence and stability of standing waves for the mixed dispersion nonlinear Schrödinger equation with a partial...
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Interaction Behaviors Between Solitons, Breathers and Their Hybrid Forms for a Short Pulse Equation
In this article, we investigate the dynamical interaction behavior of a short pulse equation in optical fibers with fast-varying packets. We...
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Boundary-Value Problems for the Evolutionary Schrödinger Equation. I
We study boundary-value problem for the evolutionary Schrödinger equation and present a survey of the works in this field.
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Riemann–Hilbert method for multi-soliton solutions of a fifth-order nonlinear Schrödinger equation
A fifth-order nonlinear Schrödinger equation which describes the one-dimensional anisotropic Heisenberg ferromagnetic spin chain is under...
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Fundamental Solutions for the Generalised Third-Order Nonlinear Schrödinger Equation
In this article, we establish exact solutions for the generalised third-order nonlinear Schrödinger equation. The elliptic function expansion and...
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On the structure of the Nehari set associated to a Schrödinger-Poisson system with prescribed mass: old and new results
In this paper we apply the fibering method of Pohozaev and the notion of extremal values introduced by Il’yasov to a Schrödinger—Poisson system, with...
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Spatiotemporal Soliton Interaction of Saturable Nonlinear Schrödinger Equations in Spatial Dimensions Higher Than 1
We derive an expression for the collision-induced amplitude dynamics in a fast collision between two ( N + 1) −dimensional spatiotemporal solitons in...
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Dispersion-constrained martingale Schrödinger problems and the exact joint S&P 500/VIX smile calibration puzzle
We solve for the first time a longstanding puzzle of quantitative finance that has often been described as the holy grail of volatility modelling:...
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Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation
In this paper, we shall solve a time-fractional nonlinear Schrödinger equation by using the quintic non-polynomial spline and the L 1 formula. The...
