𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Sharp Lr asymptotics of the small solutions to the nonlinear Schrödinger equations

✍ Scribed by Naoyasu Kita


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
152 KB
Volume
52
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis


This paper studies the large time behavior of the small solution to the nonlinear Schr odinger equation with power type nonlinearity. If the power is large enough, then it is well known that the nonlinear solution asymptotically behaves like a linear solution as t → ± ∞ (see e.g.


📜 SIMILAR VOLUMES


Exponentially small asymptotics of solut
✍ A.H. Vartanian 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 492 KB

The matrix Riemann-Hilbert factorization approach is used to derive the leading-order, exponentially small asymptotics as t --\* +oo such that x/t ~ O(1) of solutions to the Cauchy problem for the defocusing nonlinear Schr6dinger equation, iOtu + 02xu -2([ul 2 -1)u = 0, with finite density initial d

Asymptotic Expansion of the Solution to
✍ Takeshi Wada 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 164 KB

This paper deals with the equation Here, u is a complex-valued function of (t, x) # R\_R n , n 2, and \* is a real number. If u 0 is small in L 2, s with s>(nÂ2)+2, then the solution u(t) behaves asymptotically as uniformly in R n as t Ä . Here , is a suitable function called the modified scatteri