The fourth order nonlinear Schrodinger limit for quantum Zakharov system

TL;DR

This paper investigates the quantum Zakharov system and demonstrates that as ionic sound speed increases infinitely, its solution converges to that of a quantum modified nonlinear Schrödinger equation, revealing a limiting behavior.

Contribution

It establishes the convergence of the quantum Zakharov system to a quantum modified nonlinear Schrödinger equation in the high ionic sound speed limit.

Findings

Convergence of solutions as ionic sound speed tends to infinity

Derivation of the quantum modified nonlinear Schrödinger equation

Analysis of the limiting behavior of the quantum Zakharov system

Abstract

This paper is concerned with the quantum Zakharov system. We prove that when the ionic speed of sound goes to infinity, the solution to the fourth order Schrodinger part of the quantum Zakharov system converges to the solution to quantum modified nonlinear Schrodinger eqaution.