TY - JOUR
T1 - Nonlinear scattering for a system of nonlinear Klein-Gordon equations
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
AU - Wibowo, Ratno Bagus Edy
N1 - Funding Information:
The work of P.I.N. is partially supported by CONACYT. We are grateful to an unknown referee for many useful suggestions and comments.
PY - 2008
Y1 - 2008
N2 - We consider the initial value problem for systems of nonlinear Klein-Gordon equations with quadratic nonlinearities. We prove the existence of scattering states, namely, the asymptotic stability of small solutions in the neighborhood of the free solutions for small initial data in the weighted Sobolev space H4,3(R3) × H3,3(R3). If nonlinearities satisfy the strong null condition, then the same result is true in two space dimensions for small initial data in H5,4(R2) × H4,4(R2). A system of massive Dirac-massless Klein-Gordon equations in three space dimensions is also considered by our method.
AB - We consider the initial value problem for systems of nonlinear Klein-Gordon equations with quadratic nonlinearities. We prove the existence of scattering states, namely, the asymptotic stability of small solutions in the neighborhood of the free solutions for small initial data in the weighted Sobolev space H4,3(R3) × H3,3(R3). If nonlinearities satisfy the strong null condition, then the same result is true in two space dimensions for small initial data in H5,4(R2) × H4,4(R2). A system of massive Dirac-massless Klein-Gordon equations in three space dimensions is also considered by our method.
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U2 - 10.1063/1.2990493
DO - 10.1063/1.2990493
M3 - Article
AN - SCOPUS:55349101632
SN - 0022-2488
VL - 49
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 10
M1 - 103501
ER -