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Multi solitary waves for a fourth order nonlinear Schrödinger type equation

Institution:	1. Department of Mathematics, Federal University of Pampa, 97650-000 Itaqui, Brazil;2. Department of Mathematics, Federal University of São Carlos, PO B 676, 13565-905 São Carlos, Brazil;1. School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong, 510631, PR China;2. School of Mathematics, South China University of Technology, Guangzhou, Guangdong, 510641, PR China;3. Department of Mathematics, Champlain College Saint-Lambert, Quebec, J4P 3P2, Canada;4. Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 2K6, Canada;1. School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong, 510631, PR China;2. School of Mathematics, South China University of Technology, Guangzhou, Guangdong, 510641, PR China;3. Department of Mathematics, Champlain College Saint-Lambert, Quebec, J4P 3P2, Canada;4. Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 2K6, Canada;1. Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy;2. Dipartimento di Scienza e Alta Tecnologia, Università dell''Insubria, Via Valleggio, 11, 22100 Como, Italy;3. Facoltà di Ingegneria, Università Telematica Internazionale Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy;4. Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via R. Cozzi, 53, 20125 Milano, Italy;1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China;2. Faculty of Information Technology, Macau University of Science and Technology, Macau, China

Abstract:	In this article we prove the existence of multi solitary waves of a fourth order Schrödinger equation (4NLS) which describes the motion of the vortex filament. These solutions behave at large time as sum of stable Hasimoto solitons. It is obtained by solving the system backward in time around a sequence of approximate multi solitary waves and showing convergence to a solution with the desired property. The new ingredients of the proof are modulation theory, virial identity adapted to 4NLS and energy estimates. Compare to NLS, 4NLS does not preserve Galilean transform which contributes the main difficulty in spectral analysis of the corresponding linearized operator around the Hasimoto solitons.

Keywords:	Multi solitary waves Fourth order Schrödinger equation Vortex filament
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