Energy transfer model and large periodic boundary value problem for the quintic nonlinear Schrödinger equations

Hideo Takaoka

doi:10.3934/dcds.2020283

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2020, Volume 40, Issue 11: 6371-6398. Doi: 10.3934/dcds.2020283

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Energy transfer model and large periodic boundary value problem for the quintic nonlinear Schrödinger equations

Hideo Takaoka

Department of Mathematics, Kobe University, Kobe, 657-8501, Japan

Received: December 2019

Revised: June 2020

Published: July 2020

This work was supported by JSPS KAKENHI Grant Number 18H01129

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Abstract

We study the dynamics and energy exchanges between a linear oscillator and a nonlinear interaction state for the one dimensional, quintic nonlinear Schrödinger equation. Grébert and Thomann [9] proved that there exist solutions with initial data built on four Fourier modes, that confirm the conservative exchange of wave energy. Captured multi resonance in multiple Fourier modes, we simulate a similar energy exchange in long-period waves.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 42B37.

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References

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