TY - JOUR
T1 - Modified wave operator for schrÖdinger type equations with subcritical dissipative nonlinearities
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
N1 - Funding Information:
The work of P.I.N. is partially supported by CONACYT.
Publisher Copyright:
© 2007 AIMSciences.
PY - 2007
Y1 - 2007
N2 - We construct the modified wave operator for the nonlinear Schrödinger type equations (Formula presented), for (t, x) ∈ R × R. We find the solutions in the neighborhood of suitable approximate solutions provided that β ≥ 2, Im λ > 0 and ρ < 3 is sufficiently close to 3. Also we prove the time decay estimate of solutions (Formula presented). When we prove the existence of a modified scattering operator, then a natural inverse problem arises to reconstruct the parameters β, λ and ρ from the modified scattering operator.
AB - We construct the modified wave operator for the nonlinear Schrödinger type equations (Formula presented), for (t, x) ∈ R × R. We find the solutions in the neighborhood of suitable approximate solutions provided that β ≥ 2, Im λ > 0 and ρ < 3 is sufficiently close to 3. Also we prove the time decay estimate of solutions (Formula presented). When we prove the existence of a modified scattering operator, then a natural inverse problem arises to reconstruct the parameters β, λ and ρ from the modified scattering operator.
KW - Asymptotics of solutions
KW - Nonlinear schrödinger equations
KW - Subcritical nonlinearities
KW - Wave operators
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U2 - 10.3934/ipi.2007.1.391
DO - 10.3934/ipi.2007.1.391
M3 - Article
AN - SCOPUS:34548848638
SN - 1930-8337
VL - 1
SP - 391
EP - 398
JO - Inverse Problems and Imaging
JF - Inverse Problems and Imaging
IS - 2
ER -