### Abstract

We study the initial value problem for the quadratic nonlinear Klein-Gordon equation Lu = 〈i∂_{x}〉^{-1} u^{-2}, (t,x) ∈ R × R, u(0,x ) = u_{0}(x), x ∈ R, where L = ∂_{t} + i〈i∂_{x} 〉 and 〈i∂ _{x}〉 = 1 - ∂^{2} _{x}. Using the Shatah normal forms method, we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.

Original language | English |
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Article number | 504324 |

Journal | Advances in Mathematical Physics |

DOIs | |

Publication status | Published - 2010 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Applied Mathematics

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## Cite this

Hayashi, N., & Naumkin, P. I. (2010). The initial value problem for the quadratic nonlinear Klein-Gordon equation.

*Advances in Mathematical Physics*, [504324]. https://doi.org/10.1155/2010/504324