The Initial Value Problem for the Quadratic Nonlinear Klein-Gordon Equation
We study the initial value problem for the quadratic nonlinear Klein-Gordon equation ℒ𝑢=⟨𝑖𝜕𝑥⟩−1𝑢2, (𝑡,𝑥)∈𝐑×𝐑, 𝑢(0,𝑥)=𝑢0(𝑥), 𝑥∈𝐑, where ℒ=𝜕𝑡+𝑖⟨𝑖𝜕𝑥⟩ and ⟨𝑖𝜕𝑥⟩=1−𝜕2𝑥. Using the Shatah normal forms method, we obtain a sharp asymptotic behavior of small solutions without the condition of a compact suppor...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/504324 |
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