A Rogue-Langmuir-type traveling wave continuous solution to nonlinearly dispersive Schr\"{o}dinger equation using a polynomial expansion scheme

TL;DR

This paper derives a new rogue-Langmuir-type traveling wave solution for a nonlinear dispersive Schrödinger equation using polynomial expansion, demonstrating potential for quantum applications.

Contribution

It introduces a novel polynomial expansion scheme to find continuous traveling wave solutions to a nonlinear dispersive Schrödinger equation.

Findings

Derived a rogue-Langmuir-type traveling wave solution

Showed the solution's applicability to quantum well problems

Provided evidence for continuous solutions in quantum systems

Abstract

In this paper, traveling wave solutions to the nonlinearly dispersive Schr\"odinger equation are given in the case of one-dimensional non-relativistic electron confined to a cylindrical quantum well. Investigations gave evidence to the possibility of implementing continuous solutions for a quantum-based problem.