Results 21 to 30 of about 1,785 (116)
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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Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities
Advances in Nonlinear Analysis, 2015 This paper proves existence and stability of solitary-wave solutions of a system of 2-coupled nonlinear Schrödinger equations with power-type nonlinearities arising in several models of modern physics. The existence of vector solitary-wave solutions (i.e.
Bhattarai Santosh
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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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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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Dynamics on resonant clusters for the quintic non linear Schr\"odinger equation [PDF]
, 2012 We construct solutions to the quintic nonlinear Schr\"odinger equation on the circle with initial conditions supported on arbitrarily many different resonant clusters.
Haus, Emanuele, Thomann, Laurent
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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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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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