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
Instabilities of standing waves and positivity in traveling waves to a higher‐order Schrödinger equation
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DOI: 10.1002/mma.10315
Abstract: The aim of this paper is to explore a Schrödinger equation that incorporates a higher‐order operator. Traditional models for electron dynamics have utilized a second‐order diffusion Schrödinger equation, where oscillatory behavior is achieved through complex… read more here.
Keywords: equation; higher order; schr dinger; dinger equation ... See more keywords
Existence of stable standing waves for the critical fractional Schrödinger equation with an inhomogeneous combined nonlinearity
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DOI: 10.1002/mma.10335
Abstract: We study the orbitally stability of standing waves for the L2$$ {L}^2 $$ ‐critical inhomogeneous combined source term fractional nonlinear Schrödinger equation: i∂tu−(−Δ)su+a|x|−b|u|pu+|u|4sNu=0,(t,x)∈ℝ×ℝN$$ i{\partial}_tu-{\left(-\Delta \right)}^su+a{\left|x\right|}^{-b}{\left|u\right|}^pu+{\left|u\right|}^{\frac{4s}{N}}u=0,\left(t,x\right)\in \mathrm{\mathbb{R}}\times {\mathrm{\mathbb{R}}}^N $$ where N2N−1 read more here.
Keywords: x0005e; schr dinger; inhomogeneous combined; dinger equation ... See more keywords
Normalized Sign‐Changing Solutions for the Nonlinear Schrödinger Equation With a Mass‐Critical Perturbation
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DOI: 10.1002/mma.10954
Abstract: We investigate the mass‐critical perturbed nonlinear Schrödinger equation with a prescribed mass and establish the existence of sign‐changing normalized solutions in noncompact settings for N≥4$$ N\ge 4 $$ . Additionally, we analyze the asymptotic behavior… read more here.
Keywords: schr dinger; sign changing; normalized solutions; dinger equation ... See more keywords
Transmutation Operators Associated With an Angular SchröDinger‐Type Operator
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DOI: 10.1002/mma.11124
Abstract: In this work, we study the time‐independent homogeneous Schrödinger equation Δ−q(θ)r2u=0$$ \left(\Delta -\frac{q\left(\theta \right)}{r^2}\right)u=0 $$ in a bounded domain Ω⊂ℂ$$ \Omega \subset \mathbb{C} $$ . We assume the potential q$$ q $$ is a continuously… read more here.
Keywords: operator; schr dinger; schr; transmutation ... 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;
Logarithmic Stabilization of the Schrödinger Equation With Dynamic Boundary Condition
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DOI: 10.1002/mma.70235
Abstract: This paper addresses the stabilization problem for the Schrödinger equation with dynamic boundary condition of Wentzell type. Under suitable assumption about the damping domain, we demonstrate that sufficiently smooth solutions of the Schrödinger equation decay… read more here.
Keywords: equation; schr dinger; equation dynamic; boundary condition ... See more keywords
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