Abstract
This paper is devoted to the theoretical analysis of a coupled nonlinear system of fractional Schrödinger equations in Rn×R+,n≥1, considering time fractional derivative in the Caputo sense, and a fractional spatial dispersion defined in terms of the Fourier transform. We prove the existence of local and global mild solutions, as well as the asymptotic stability of global mild solutions, considering power-type nonlinearities and initial data in the framework of weak-Lp spaces, which contain singular functions with infinite energy. As consequence of the embedding of weak-Lp spaces in Lloc2, for p>2, the obtained solutions have finite local L2-mass. In addition, we discuss the scenario in which it is possible to obtain the existence of self-similar solutions, which is a symmetric property that reproduces the structure of physical phenomena in different spatio-temporal scales. Our results are applicable, in the fractional setting, to the nonlinear Schrödinger and Biharmonic equations, as well as in a large class of dispersive systems appearing in nonlinear optics.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Partial Differential Equations in Applied Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
