Hamiltonian form of extended cubic-quintic nonlinear Schr\"{o}dinger equation in a nonlinear Klein-Gordon model

TL;DR

This paper derives a Hamiltonian-structured extended cubic-quintic nonlinear Schrödinger equation within a nonlinear Klein-Gordon framework, highlighting how nonlinear balance affects wave stability.

Contribution

It introduces a Hamiltonian form of the extended cubic-quintic nonlinear Schrödinger equation considering high-order nonlinear effects in a Klein-Gordon model.

Findings

Changing cubic-quintic balance impacts wave packet stability.

High-order nonlinear effects are incorporated via Hamiltonian perturbation.

The model provides insights into nonlinear wave modulation stability.

Abstract

We derive an extended cubic-quintic nonlinear Schr\"{o}dinger equation with Hamiltonian structure in a nonlinear Klein-Gordon model with cubic-quintic nonlinearity. We use the nonlinear dispersion relation to properly take into account the input of high-order nonlinear effects in the Hamiltonian perturbation approach to nonlinear modulation. We demonstrate that changing the balance between the cubic and quintic nonlinearities has a significant effect on the stability of unmodulated wave packets to long-wave modulations.