## Differential and Integral Equations

- Differential Integral Equations
- Volume 10, Number 3 (1997), 499-520.

### Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension

#### Abstract

We prove that for small initial data there exist unique global solutions to a certain special class of nonlinear Klein-Gordon equations with cubic nonlinearity in one space dimension, which asymptotically approach the free solution of the linear Klein-Gordon equation as $t \to + \infty$.

#### Article information

**Source**

Differential Integral Equations, Volume 10, Number 3 (1997), 499-520.

**Dates**

First available in Project Euclid: 2 May 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1367525665

**Mathematical Reviews number (MathSciNet)**

MR1744859

**Zentralblatt MATH identifier**

0892.35136

**Subjects**

Primary: 35L70: Nonlinear second-order hyperbolic equations

Secondary: 35L10: Second-order hyperbolic equations

#### Citation

Moriyama, Kazunori. Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension. Differential Integral Equations 10 (1997), no. 3, 499--520. https://projecteuclid.org/euclid.die/1367525665