Nakao Hayashi, Pavel I. Naumkin
We study the initial-value problem for the quadratic nonlinear Schrodinger equation
For small initial data we prove that there exists a unique global solution of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region by the self-similar solution such that the total mass
and in the far region the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.
Submitted March 19, 2007. Published February 1, 2008.
Math Subject Classifications: 35B40, 35Q55.
Key Words: Nonlinear Schrodinger equation; large time asymptotic; self-similar solutions.
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| Nakao Hayashi |
Department of Mathematics, Graduate School of Science
Osaka University, Osaka
Toyonaka, 560-0043, Japan
| Pavel I. Naumkin |
Instituto de Matemáticas
Universidad Nacional Autónoma de México
Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico
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