TY - JOUR
T1 - The initial value problem for the quadratic nonlinear Klein-Gordon equation
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
PY - 2010
Y1 - 2010
N2 - 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 ) = u0(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.
AB - 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 ) = u0(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.
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U2 - 10.1155/2010/504324
DO - 10.1155/2010/504324
M3 - Article
AN - SCOPUS:84868380439
SN - 1687-9120
JO - Advances in Mathematical Physics
JF - Advances in Mathematical Physics
M1 - 504324
ER -