Results 21 to 30 of about 147 (118)
Darboux transformation for classical acoustic spectral problem
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 49, Page 3123-3142, 2003., 2003 We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows steps similar to those for the Schrödinger operator. However, there is no one‐to‐one correspondence between the two problems.
A. A. Yurova, A. V. Yurov, M. Rudnev
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Optimal Interpolation Constant for the Generalized Schrödinger-Newton System [PDF]
, 2015 2010 Mathematics Subject Classification: 35A05, 35A15, 35Q51 ...
Georgiev, Vladimir, Venkov, George
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The trajectory‐coherent approximation and the system of moments for the Hartree type equation
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 6, Page 325-370, 2002., 2002 The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB‐Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ℏ (ℏ → 0), are constructed with a power accuracy of O(ℏ N/2), where N is any natural number.
V. V. Belov +2 more
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Mechanical analogy for the wave‐particle: helix on a vortex filament
Journal of Applied Mathematics, Volume 2, Issue 5, Page 241-263, 2002., 2002 The small amplitude‐to‐thread ratio helical configuration of a vortex filament in the ideal fluid behaves exactly as de Broglie wave. The complex‐valued algebra of quantum mechanics finds a simple mechanical interpretation in terms of differential geometry of the space curve.
Valery P. Dmitriyev
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Finite difference scheme for a high order nonlinear Schrödinger equation with localized damping [PDF]
, 2019 In this work we present a finite difference scheme used to solve a High order Nonlinear Schrödinger Equation. These equations can model the propagation of solitons travelling in fiber optics ([3], [11]).
SEPÚLVEDA C., Mauricio A. +3 more
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On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 7, Page 375-394, 2001., 2001 We consider the Cauchy problem periodic in the spatial variable for the usual cubic nonlinear Schrödinger equation and construct an infinite sequence of invariant measures associated with higher conservation laws for dynamical systems generated by this problem on appropriate phase spaces.
Peter E. Zhidkov
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On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions
Abstract and Applied Analysis, Volume 6, Issue 6, Page 329-338, 2001., 2001 For stationary Schrödinger equation in ℝ n with the finite potential the singular pseudopotential is constructed in the form allowing us to find wave functions. The method does not require the knowledge of the explicit form of a potential and assumes only knowledge of the scattering amplitude for fixed level of energy.
Yuriy Valentinovich Zasorin
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Modulation type spaces for generators of polynomially bounded groups and Schrödinger equations [PDF]
, 2018 We introduce modulation type spaces associated with the generators of polynomially bounded groups. Besides strongly continuous groups we study in detail the case of bi-continuous groups, e.g. weak-continuous groups in dual spaces.
Kunstmann, Peer Christian
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Attractors of semigroups associated with nonlinear systems for diffusive phase separation
Abstract and Applied Analysis, Volume 1, Issue 2, Page 169-192, 1996., 1996 We consider a model for diffusive phase transitions, for instance, the component separation in a binary mixture. Our model is described by two functions, the absolutete temperature θ : = θ(t, x) and the order parameter w : = w(t, x), which are governed by a system of two nonlinear parabolic PDEs.
Nobuyuki Kenmochi
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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.In this paper, we consider the initial value problem associated with the cubic nonlinear Schrödinger equation with third‐order dispersion ∂tu+iα∂x2u+β∂x3u+iγu2u=0,x∈ℝ,t∈ℝ,ux,0=u0x, where α, β and γ are real constants such that β, γ ≠ 0, u is a complex valued function and the initial data u0 is analytic on ℝ and has a uniform radius of analyticity σ0 in
Tegegne Getachew, Xiasheng Shi
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