## Differential and Integral Equations

- Differential Integral Equations
- Volume 25, Number 7/8 (2012), 685-698.

### Global existence of solutions to nonlinear dispersive wave equations

Nakao Hayashi, Seishirou Kobayashi, and Pavel I. Naumkin

#### Abstract

We study the global existence of solutions to nonlinear dispersive wave equations \begin{equation*} \partial _{t}^{2}u+\frac{1}{\rho ^{2}}\left\vert \partial _{x}\right\vert ^{2\rho }u=\lambda \left\vert \partial _{t}u\right\vert ^{p-1}\partial _{t}u \end{equation*} in one space dimension, where $0<\rho \leq 2,\rho \neq 1,p>3$ and $\lambda \in \mathbf{C}.$

#### Article information

**Source**

Differential Integral Equations, Volume 25, Number 7/8 (2012), 685-698.

**Dates**

First available in Project Euclid: 20 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356012658

**Mathematical Reviews number (MathSciNet)**

MR2975690

**Zentralblatt MATH identifier**

1265.35331

**Subjects**

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

#### Citation

Hayashi, Nakao; Kobayashi, Seishirou; Naumkin, Pavel I. Global existence of solutions to nonlinear dispersive wave equations. Differential Integral Equations 25 (2012), no. 7/8, 685--698. https://projecteuclid.org/euclid.die/1356012658