The Cauchy Problem for the Nonlinear Schrödinger Equation With a Convolution Potential

Esfahani A. Tesfahun A.
October 2025 John Wiley and Sons Inc

Studies in Applied Mathematics
2025 #155 Issue 4

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 space linked to the energy. Additionally, we derive conditions under which the solutions are uniformly bounded in the energy space. This finding is closely linked to the existence of standing waves for this equation.

dispersive estimates , local well-posedness , standing waves , uniform boundedness

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Department of Mathematics, Nazarbayev University, Astana, Kazakhstan

Department of Mathematics

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