Results 21 to 30 of about 1,815 (116)
Variational approach to dynamics of bright solitons in lossy optical fibers
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 49, Page 3143-3148, 2003., 2003 A variational analysis of dynamics of soliton solution of coupled nonlinear Schrödinger equations with oscillating terms is made, considering a birefringent fiber with a third‐order nonlinearity in the anomalous dispersion frequency region. This theoretical model predicts optical soliton oscillations in lossy fibers.
M. F. Mahmood, S. Brooks
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A note on asymptotic helix and quantum mechanical structure
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 48, Page 3031-3039, 2003., 2003 Using the formulation of a moving curve, we demonstrate that an asymptotic helix goes over to the linear time‐dependent Schrödinger equation as shown by Dmitriyev (2002).
Partha Guha
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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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Well-posedness for the fourth-order Schrödinger equations with quadratic nonlinearity
Advances in Differential Equations, 2011 This paper is concerned with 1-D quadratic semilinear fourth-order Schrödinger equations. Motivated by the quadratic Schrödinger equations in the pioneer work of Kenig-Ponce-Vega [12], three bilinearities uv, uv, uv for functions u, v : R× [0, T ] 7→ C ...
Jiqiang Zheng
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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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Remarks on the blow-up for the Schr\ [PDF]
, 2004 In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrodinger equation with Dirichlet boundary condi- tions, posed on a plane domain.
V. Banica
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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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Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction
Advances in Nonlinear Analysis, 2021 In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region
Wang Jun
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MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS
Forum of Mathematics, Pi, 2015 We consider the cubic nonlinear Schrödinger equation posed on the spatial domain $\mathbb{R}\times \mathbb{T}^{d}$. We prove modified scattering and construct modified wave operators for small initial and final data respectively ($1\leqslant d\leqslant 4$
ZAHER HANI +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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