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Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation
The authors study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus (KE for short) equation and construct the long time asymptotic...
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The solvability of a kind of generalized Riemann–Hilbert problems on function spaces \(H_{\ast }\)
In this paper, we study a kind of generalized Riemann–Hilbert problems (R-HPs) with several unknown functions in strip domains. We mainly discuss...
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Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions
In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix...
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The Nodal LTSN Solution and a New Approach to Determine the Outgoing Angular Flux at the Boundary in a Rectangular Domain
In this work, we present the Nodal LTS N 2D solution using a new approach to determine the unknown but necessary angular fluxes at the domain...
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Morphodynamic Modelling in Marine Environments: Model Formulation and Solution Techniques
The bathymetry and geometry of coastal seas, barrier coasts and estuaries strongly influence tides and currents, and the associated transport of...
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Global smoothing for the Davey–Stewartson system on \(\mathbb {R}^2\)
In this paper, we study the regularity properties of solutions to the Davey–Stewartson system. It is shown that for initial data in a Sobolev space,...
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Interval-valued picture fuzzy hypergraphs with application towards decision making
The concept of interval-valued picture fuzzy sets (IVPFSs) is the most generalized form of fuzzy sets (FSs) and is proven a useful tool to manipulate...
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Adapted Metrics for Singular Hyperbolic Flows
Singular and sectional-hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with...
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Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall
We develop a theory of enhanced diffusivity and skewness of the longitudinal distribution of a diffusing tracer advected by a periodic time-varying...
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Scattering problems for the wave equation in 1D: D’Alembert-type representations and a reconstruction method
We derive the extension of the classical d’Alembert formula for the wave equation, which provides the analytical solution for the direct scattering...
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Holomorphic solutions and solvability theory for a class of linear complete singular integro-differential equations with convolution by Riemann–Hilbert method
In this article, we investigate a class of linear complete singular integro-differential equations of convolution type with Fredholm integral...
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Persistence of heterodimensional cycles
A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their...
