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| journal = Inverse Problems

| title = Asymptotic analysis of soliton problems. An inverse scattering approach

| journal = Inverse Problems

...ering transform for the Benjamin-Ono equation: a pivot to multidimensional problems

...ring transform for the Benjamin-Ono equation---a pivot to multidimensional problems

| jpage = Inverse problems: theory and applications (Cortona/Pisa, 2002), 137--146

| title = The inverse scattering transform-Fourier analysis for nonlinear problems

| title = Direct and inverse scattering for the nonlinear Schrödinger equation with a potential | jpage = VI Seminar on Free Boundary Value Problems and their Applications, Part 1 (Spanish) (Rosario, 1998), 13--20

** For initial data equal to a delta function there are serious problems with existence and uniqueness [[KnPoVe2001]]. ** For large Schwartz data, these asymptotics can be obtained by inverse scattering methods [[ZkMan1976]], [[SeAb1976]], [[No1980]], [[DfZx1994]]

** For small smooth data this was achieved by inverse scattering techniques in [[FsSng1992]], [[Zx1990]] ...<math>{\Bbb T} \times {\Bbb R}</math> in [[SauTz2001]]. The corresponding problems for <math>{\Bbb R} \times {\Bbb T}</math> and <math>{\Bbb T} \times {\Bbb T

...rch/events/2008_2009/workshops/pde-courses Nonlinear PDE and free boundary problems] ...rspages.php?task=displayevent&event_id=10w5066 Analysis and Boundary Value Problems on Real and Complex Domains]

* If <math>V\,</math>grows faster than quadratic, then there are significant problems due to the failure of smoothness of the fundamental solution; if <math>V\,< ...y potential in <math>L^p\,</math> for <math>p \ge d/2\,,</math> as well as inverse square potentials <math>1/|x|^2\,,</math> and linear combinations of these,

.... Segur, ''The inverse scattering transform-Fourier analysis for nonlinear problems'', Studies in Appl. Math. '''53''' (1974), no. 4, 249-315. ...ring transform for the Benjamin-Ono equation, a pivot for multidimensional problems'', Stud. Appl. Math. '''68''' (1983), 1-10.