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Asymptotic Expansion of the Solution to the Nonlinear Schrödinger Equation with Nonlocal Interaction

✍ Scribed by Takeshi Wada

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
164 KB
Volume
180
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 scattering state, and the functions S , 1, j , j=0, 1, 2, are represented explicitly by using ,.

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