Stability of Big Solitons in a Competitive Power Nonlinear Schr\"odinger Equation

TL;DR

This paper establishes the existence and orbital stability of large solitons in a competitive power nonlinear Schrödinger equation, introducing a novel approach to fix soliton frequency and constructing multi-solitons with different speeds.

Contribution

It provides the first proof of existence and stability of big solitons depending on frequency in a competitive nonlinear Schrödinger equation, solving an open problem in normalized solutions.

Findings

Existence of stable big solitons depending on frequencies.

Construction of multi-solitons with different speeds.

Solution to an open problem in normalized solutions.

Abstract

By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinear Schr\"odinger equations is found, and an open problem in normalized solutions is answered. Then existence and orbital stability of big solitons depending on frequencies for nonlinear Schr\"odinger equation with competitive power nonlinearity is proved for the first time. In addition multi-solitons of the equation with different speeds are constructed by stable big solitons.