Superdiffusive fractional in time Schrodinger equations: A unifying approach to superdiffusive waves

Luis Caicedo Torres; Ciprian G. Gal

doi:10.1016/j.cnsns.2023.107141

Superdiffusive fractional in time Schrodinger equations: A unifying approach to superdiffusive waves

Luis Caicedo Torres
, Ciprian G. Gal

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We consider a mathematical model for the behavior of superdiffusive waves in a physical regime that interpolates continuously between the Schrodinger equation and the wave equation, respectively. Our main goal is to develop a unifying mathematical framework establishing the well-posedness of superdiffusive wave solutions to the corresponding linear and nonlinear models, associated with (pseudo) Hamiltonian systems acting on a given (locally-compact) metric space X, and to further analyze their regularity properties.

Original language	English
Article number	107141
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	120
DOIs	https://doi.org/10.1016/j.cnsns.2023.107141
State	Published - Jun 2023
Externally published	Yes

Keywords

Anomalous waves
Caputo derivative
Fractals
Fractional in time derivatives
Quantum mechanics
Riemannian geometry
Schrodinger equations
Superdiffusive waves

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10.1016/j.cnsns.2023.107141

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title = "Superdiffusive fractional in time Schrodinger equations: A unifying approach to superdiffusive waves",

abstract = "We consider a mathematical model for the behavior of superdiffusive waves in a physical regime that interpolates continuously between the Schrodinger equation and the wave equation, respectively. Our main goal is to develop a unifying mathematical framework establishing the well-posedness of superdiffusive wave solutions to the corresponding linear and nonlinear models, associated with (pseudo) Hamiltonian systems acting on a given (locally-compact) metric space X, and to further analyze their regularity properties.",

keywords = "Anomalous waves, Caputo derivative, Fractals, Fractional in time derivatives, Quantum mechanics, Riemannian geometry, Schrodinger equations, Superdiffusive waves",

author = "Torres, \{Luis Caicedo\} and Gal, \{Ciprian G.\}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2023",

month = jun,

doi = "10.1016/j.cnsns.2023.107141",

language = "English",

volume = "120",

journal = "Communications in Nonlinear Science and Numerical Simulation",

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TY - JOUR

T1 - Superdiffusive fractional in time Schrodinger equations

T2 - A unifying approach to superdiffusive waves

AU - Torres, Luis Caicedo

AU - Gal, Ciprian G.

PY - 2023/6

Y1 - 2023/6

N2 - We consider a mathematical model for the behavior of superdiffusive waves in a physical regime that interpolates continuously between the Schrodinger equation and the wave equation, respectively. Our main goal is to develop a unifying mathematical framework establishing the well-posedness of superdiffusive wave solutions to the corresponding linear and nonlinear models, associated with (pseudo) Hamiltonian systems acting on a given (locally-compact) metric space X, and to further analyze their regularity properties.

AB - We consider a mathematical model for the behavior of superdiffusive waves in a physical regime that interpolates continuously between the Schrodinger equation and the wave equation, respectively. Our main goal is to develop a unifying mathematical framework establishing the well-posedness of superdiffusive wave solutions to the corresponding linear and nonlinear models, associated with (pseudo) Hamiltonian systems acting on a given (locally-compact) metric space X, and to further analyze their regularity properties.

KW - Anomalous waves

KW - Caputo derivative

KW - Fractals

KW - Fractional in time derivatives

KW - Quantum mechanics

KW - Riemannian geometry

KW - Schrodinger equations

KW - Superdiffusive waves

UR - https://www.scopus.com/pages/publications/85147455208

U2 - 10.1016/j.cnsns.2023.107141

DO - 10.1016/j.cnsns.2023.107141

M3 - Article

AN - SCOPUS:85147455208

SN - 1007-5704

VL - 120

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 107141

ER -

Superdiffusive fractional in time Schrodinger equations: A unifying approach to superdiffusive waves

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Keywords

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