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Inhomogeneous NLS in negative Sobolev spaces via Fourier-Lebesgue and modulation spaces
Divyang G. Bhimani, Diksha Dhingra, Vijay Kumar Sohani
The purpose of this work is to provide a broader framework for analyzing the 1D mass-subcritical inhomogeneous nonlinear Schrödinger equation (INLS) \[iu_t + u_{xx} \pm |x|^{-b}|u|…
On 1D mass subcritical nonlinear Schr\''odinger and Hartree equations in modulation spaces
Divyang G. Bhimani, Diksha Dhingra, Vijay Kumar Sohani
We establish well-posedness theory for the 1D mass-subcritical nonlinear Schrödinger equation (NLS) having power-type nonlinearity in a certain modulation spaces $M^{p…
Fractional nonlinear Schrödinger and Hartree equations in modulation spaces
Divyang G. Bhimani, Diksha Dhingra, Vijay Kumar Sohani
We establish global well-posedness for the mass subcritical nonlinear fractional Schrödinger equation having radial initial data in modulation sp…
Low-regularity global solution of the inhomogeneous nonlinear Schrödinger equations in modulation spaces
Divyang G. Bhimani, Diksha Dhingra, Vijay Kumar Sohani
The study of low regularity Cauchy data for nonlinear dispersive PDEs has successfully been achieved using modulation spaces in recent years. In this paper, we study the…
Nonlinear Schrödinger equation for the twisted Laplacian in the critical case
Vijay Kumar Sohani
We prove well-posedness of solution to the nonlinear Schrödinger equation associated to the twisted Laplacian on $\C^n$ for a general class of nonlinearities including power type w…
Nonlinear Schrödinger equation for the twisted Laplacian
P. K. Ratnakumar, Vijay Kumar Sohani
We establish the local well posedness of solution to the nonlinear Schrödinger equation associated to the twisted Laplacian on $\C^n$ in certain first order Sobolev space. Our appr…