Multi-existence of multi-solitons for the supercritical nonlinear Schrödinger equation in one dimension (Q379856)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Multi-existence of multi-solitons for the supercritical nonlinear Schrödinger equation in one dimension |
scientific article; zbMATH DE number 6224716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multi-existence of multi-solitons for the supercritical nonlinear Schrödinger equation in one dimension |
scientific article; zbMATH DE number 6224716 |
Statements
Multi-existence of multi-solitons for the supercritical nonlinear Schrödinger equation in one dimension (English)
0 references
11 November 2013
0 references
nonlinear Schrödinger equation
0 references
multi-solitons
0 references
supercritical growth
0 references
asymptotic behaviour
0 references
instability
0 references
0 references
0 references
0 references
0 references
0 references
0 references
The author considers the supercritical nonlinear Schrödinger equation in dimension 1 NEWLINE\[NEWLINE i \partial_t u + \partial^2_x u + |u|^{p-1} u = 0 NEWLINE\]NEWLINE with \(u(0) = u_0 \in H^1(R)\), where \(p>5\) and \(u\) a complex-valued function.NEWLINENEWLINEHe constructs for any \(N\geq 2\) an \(N\)-parameter family of solutions to the equation above, i.e. an \(N\)-parameter family of solutions whose \(H^1\) norm converges exponentially in time to the given linear combination of \(N\) solitary waves.
0 references
