We prove the existence of a new type of solutions to a nonlinear Schr ̈odinger system. These solutions, which we call multi-speeds solitary waves, behave at large time as a couple of scalar solitary waves traveling at different speeds. The proof relies on the construction of approximations of the multi-speeds solitary waves by solving the system backward in time and using energy methods to obtain uniform estimates.
Multi-speeds solitary waves solutions for nonlinear Schrödinger systems / Ianni, I; Le Coz, S. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 89:2(2014), pp. 623-639. [10.1112/jlms/jdt083]
Multi-speeds solitary waves solutions for nonlinear Schrödinger systems
IANNI I;
2014
Abstract
We prove the existence of a new type of solutions to a nonlinear Schr ̈odinger system. These solutions, which we call multi-speeds solitary waves, behave at large time as a couple of scalar solitary waves traveling at different speeds. The proof relies on the construction of approximations of the multi-speeds solitary waves by solving the system backward in time and using energy methods to obtain uniform estimates.| File | Dimensione | Formato | |
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