Results 1 to 10 of about 10,797 (309)
A Universal Asymptotic Regime in the Hyperbolic Nonlinear Schrödinger Equation [PDF]
SIAM Journal on Applied Mathematics, 2017 The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schrödinger (HNLS) equation is discussed. Based on analytical and extensive numerical simulations an approximate self-similar solution is found for a wide range of initial conditions -- essentially for initial lumps of small to ...
Mark J Ablowitz +2 more
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Complex soliton wave patterns of Gross–Pitaevskii systems: application in quantum and optical engineering [PDF]
Scientific ReportsThe purpose of this work is to explore precise solutions, particularly soliton solutions, by fractionally analyzing the multicomponent Gross–Pitaevskii problem, a basic nonlinear Schrödinger equation. Soliton solutions are essential for comprehending the
Muhammad Bilal +5 more
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Demonstratio Mathematica, 2023 In this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in the governing equations is approximated by a finite difference.
Lei Weidong +4 more
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Results in Physics, 2021 This present manuscript studies a nonlinear hyperbolic model in fractional form which generalizes the nonlinear Klein–Gordon system. The equation under investigation includes the presence of a time-fractional operator of the Caputo type.
J.E. Macías-Díaz
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On homogenization of nonlinear hyperbolic equations
Communications on Pure and Applied Analysis, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Efendiev, Yalchin, Popov, Bojan
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Complex optical solutions and modulation instability of hyperbolic Schrödinger dynamical equation
Results in Physics, 2019 Complex hyperbolic Schrödinger equation describes ultra-short pulse propagation in nonlinear media fiber optics. In this paper, new complex solutions for the complex hyperbolic Schrödinger equation are constructed using generalized elliptic equation ...
Wilson Osafo Apeanti +2 more
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Anomalous Solutions to Nonlinear Hyperbolic Equations [PDF]
, 2020 The behavior of sufficiently regular solutions to semilinear hyperbolic equations has attracted a great deal of attention in the past decades, concerning local/global existence, finite time blow-up, critical exponents, and propagation of singularities. Solutions of lower regularity may exhibit unexpected (anomalous) propagation of singularities.
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A non-linear hyperbolic equation
International Journal of Mathematics and Mathematical Sciences, 1980 In this paper the following Cauchy problem, in a Hilbert space H, is considered: (I+λA)u″+A2u+[α+M(|A12u|2)]Au=fu(0)=u0u′(0 ...
Eliana Henriques de Brito
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Journal of Function Spaces, 2022 Here, the miscellaneous soliton solutions of the generalized nonlinear Schrödinger equation are considered that describe the model of few-cycle pulse propagation in metamaterials with parabolic law of nonlinearity.
Xiaoyan Li +5 more
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Nonlinear Hyperbolic Equations in Infinite Homogeneous Waveguides [PDF]
Communications in Partial Differential Equations, 2005 In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann boundary conditions. In the case of Neumann boundary conditions we need to assume a natural nonlinear Neumann condition
Metcalfe, Jason +2 more
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