### Solutions to nonlinear higher order Schrödinger equations with small initial data on modulation spaces

Tomoya Kato

#### Abstract

In this paper, we consider the Cauchy problem for the nonlinear higher order Schrödinger equations on modulation spaces $M_{p,q}^s$ and show the existence of a unique global solution by using integrability of time decay factors of time decay estimates. As a result, we are able to deal with wider classes of a nonlinearity and a solution space. Moreover, we study time decay estimates of a semi--group $e^{it\phi(\sqrt{-\Delta})}$ with a polynomial symbol $\phi$. Considering multiplicities of critical points and inflection points of $\phi$ carefully, we have time decay estimates with better time decay rate.

#### Article information

Source
Adv. Differential Equations, Volume 21, Number 3/4 (2016), 201-234.

Dates
First available in Project Euclid: 18 February 2016