Strichartz estimates for non‐degenerate Schrödinger equations
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DOI: 10.1002/mana.201800148
Abstract: We consider the Schrödinger equation with a non‐degenerate metric on the Euclidean space. We study local in time Strichartz estimates for the Schrödinger equation without loss of derivatives including the endpoint case. In contrast to… read more here.
Keywords: dinger equation; strichartz estimates; estimates non; non degenerate ... See more keywords
Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity
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DOI: 10.1002/mma.5827
Abstract: The main aim of this article is to present some new exact solutions of the resonant nonlinear Schrödinger equation. These solutions are derived by using the generated exponential rational function method (GERFM). The kink‐type, bright,… read more here.
Keywords: dinger equation; schr dinger; nonlinear schr;
Schrödinger equation based analytic assessment of thermal properties of confined electrons under vector and scalar fields
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DOI: 10.1002/mma.7577
Abstract: In this research, we have extracted the covariant form of the Schrödinger equation in the Riemannian manifold M = ℝ3 with a position‐dependent mass (PDM) distribution in the presence of magnetic fields for each point… read more here.
Keywords: analytic assessment; equation; dinger equation; schr dinger ... See more keywords
Ground State Solutions for a Quasilinear Schrödinger Equation
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DOI: 10.1007/s00009-016-0816-3
Abstract: In this paper, we study the following quasilinear Schrödinger equation of the form $$\begin{aligned} -\Delta u+V(x)u-\Delta (u^{2})u= g(x,u),~~~ x\in \mathbb {R}^N \end{aligned}$$-Δu+V(x)u-Δ(u2)u=g(x,u),x∈RNwhere V and g are 1-periodic in $$x_{1},\ldots ,x_{N}$$x1,…,xN, and g is a superlinear… read more here.
Keywords: dinger equation; state solutions; quasilinear schr; ground state ... See more keywords
Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation
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DOI: 10.1007/s00220-017-2895-9
Abstract: AbstractFinite-gap (algebro-geometric) solutions to the focusing Nonlinear Schrödinger Equation (fNLS) 0-1$$i \psi_t + \psi_{xx} + 2|\psi|^2\psi=0,$$iψt+ψxx+2|ψ|2ψ=0,are quasi-periodic solutions that represent nonlinear multi-phase waves. In general, a finite-gap solution for (0-1) is defined by a collection… read more here.
Keywords: dinger equation; nonlinear schr; schr dinger; finite gap ... See more keywords
The Nonlinear Steepest Descent Method to Long-Time Asymptotics of the Coupled Nonlinear Schrödinger Equation
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DOI: 10.1007/s00332-017-9426-x
Abstract: The Riemann–Hilbert problem for the coupled nonlinear Schrödinger equation is formulated on the basis of the corresponding $$3\times 3$$3×3 matrix spectral problem. Using the nonlinear steepest descent method, we obtain leading-order asymptotics for the Cauchy… read more here.
Keywords: dinger equation; coupled nonlinear; nonlinear schr; schr dinger ... See more keywords
Theory of Stochastic Schrödinger Equation in Complex Vector Space
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DOI: 10.1007/s10701-017-0076-5
Abstract: A generalized Schrödinger equation containing correction terms to classical kinetic energy, has been derived in the complex vector space by considering an extended particle structure in stochastic electrodynamics with spin. The correction terms are obtained… read more here.
Keywords: stochastic schr; equation; dinger equation; schr dinger ... See more keywords
On High Dimensional Schrödinger Equation with Quasi-Periodic Potentials
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DOI: 10.1007/s10883-016-9347-2
Abstract: In this paper, we consider the high dimensional Schrödinger equation −d2ydt2+u(t)y=Ey,y∈ℝn,$ -\frac {d^{2}y}{dt^{2}} + u(t)y= Ey, y\in \mathbb {R}^{n}, $ where u(t) is a real analytic quasi-periodic symmetric matrix, E=diag(λ12,…,λn2)$E= \text {diag}({\lambda _{1}^{2}}, \ldots ,… read more here.
Keywords: high dimensional; dinger equation; dimensional schr; quasi periodic ... See more keywords
Modified two-derivative Runge–Kutta methods for the Schrödinger equation
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DOI: 10.1007/s10910-017-0830-0
Abstract: A family of modified two-derivative Runge–Kutta (MTDRK) methods for the integration of the Schrödinger equation are obtained. Two new three-stage and fifth order TDRK methods are derived. The numerical results in the integration of the… read more here.
Keywords: dinger equation; derivative runge; modified two; two derivative ... See more keywords
Pseudospectral solution of the Schrödinger equation for the Rosen-Morse and Eckart potentials
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DOI: 10.1007/s10910-019-01007-2
Abstract: Pseudospectral methods based on non-classical quadratures are used to numerically compute the eigenvalues and eigenfunctions of the Schrödinger equation for the Rosen-Morse and Eckart potentials. The method uses a basis set of non-classical polynomials, $$\{… read more here.
Keywords: dinger equation; rosen morse; equation rosen; non classical ... See more keywords
On the variational principle for the non-linear Schrödinger equation
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DOI: 10.1007/s10910-019-01082-5
Abstract: While variation of the energy functional yields the Schrödinger equation in the usual, linear case, no such statement can be formulated in the general nonlinear situation when the Hamiltonian depends on its eigenvector. In this… read more here.
Keywords: equation; dinger equation; schr dinger; energy ... See more keywords