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Journal article
Dynamics near a minimal-mass soliton for a Korteweg-de Vries equation
Dynamical systems (London, England), v 29(2)
03 Apr 2014
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Abstract
We study soliton solutions to a generalized Korteweg-de Vries (KdV) equation with a saturated nonlinearity, following the line of inquiry of Marzuola, Raynor and Simpson for the nonlinear Schrodinger equation (NLS). KdV with such a nonlinearity is known to possess a minimal-mass soliton. We consider a small perturbation of a minimal-mass soliton and numerically shadow a system of ordinary differential equation (ODEs), which models the behaviour of the perturbation for short times. This connects nicely to analytic works of Comech, Cuccagna and Pelinovsky as well as of Grimshaw and Pelinovsky. These ODEs form a simple dynamical system with a single unstable hyperbolic fixed point with two possible dynamical outcomes. A particular feature of the dynamics is that they are non-oscillatory. This distinguishes the KdV problem from the analogous NLS one.
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Details
- Title
- Dynamics near a minimal-mass soliton for a Korteweg-de Vries equation
- Creators
- J. L. Marzuola - University of North Carolina at Chapel HillS. Raynor - Wake Forest UniversityG. Simpson - Drexel University
- Publication Details
- Dynamical systems (London, England), v 29(2)
- Publisher
- Taylor & Francis
- Number of pages
- 15
- Grant note
- OISE-0967140 / NSF PIRE grant; National Science Foundation (NSF); NSF - Office of the Director (OD) NSERC; Natural Sciences and Engineering Research Council of Canada (NSERC) Simons Foundation IBM Junior Faculty Development Award through the University of North Carolina; International Business Machines (IBM) DE-SC0002085 / DOE grant; United States Department of Energy (DOE)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000334724700008
- Scopus ID
- 2-s2.0-84899476796
- Other Identifier
- 991019169657304721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical