TY - JOUR
T1 - The initial value problem for the cubic nonlinear Klein-Gordon equation
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
PY - 2008/11
Y1 - 2008/11
N2 - We study the initial value problem for the cubic nonlinear Klein-Gordon equation {utt + u-uxx = μu3,(t, x) R × R, u(0) = u0, ut(0) = u1, x R. where μ R and the initial data are real-valued functions. 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 cubic nonlinear Klein-Gordon equation {utt + u-uxx = μu3,(t, x) R × R, u(0) = u0, ut(0) = u1, x R. where μ R and the initial data are real-valued functions. 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.
KW - Asymptotics of solutions
KW - Cubic nonlinear Klein-Gordon equation
KW - Initial value problem
KW - The inverse wave modified operator
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U2 - 10.1007/s00033-007-7008-8
DO - 10.1007/s00033-007-7008-8
M3 - Article
AN - SCOPUS:55549110942
SN - 0044-2275
VL - 59
SP - 1002
EP - 1028
JO - Zeitschrift fur Angewandte Mathematik und Physik
JF - Zeitschrift fur Angewandte Mathematik und Physik
IS - 6
ER -