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math.AP2026
Sharp homogeneous Gagliardo--Nirenberg inequalities with applications to normalized solutions for a generalized MMT-type equation
Amin Esfahani, Mukhtar Karazym
In this paper, we prove the existence of optimizers for a class of sharp homogeneous Gagliardo--Nirenberg inequalities, extending the result of Bellazzini, Frank, and Visciglia \ci…
math.AP2026
Traveling Waves for Nonlocal Derivative Nonlinear Schrödinger Equations: A Variational Characterization
Amin Esfahani, Adilbek Kairzhan, Mukhtar Karazym
We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schrödinger equation with general coefficients by variational methods. We s…
math.AP2024
The Cauchy problem for the nonlinear Schrödinger equation with a convolution potential
Amin Esfahani, Achenef Tesfahun
This paper investigates the nonlinear Schrödinger equation with a singular convolution potential. It demonstrates the local well-posedness of this equation in a modified Sobolev sp…