TY - JOUR
T1 - Superdiffusive fractional in time Schrodinger equations
T2 - A unifying approach to superdiffusive waves
AU - Torres, Luis Caicedo
AU - Gal, Ciprian G.
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
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 -