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Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons
Institution:1. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;2. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China;1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil;2. Dipartimento di Matematica, Politecnico di Milano, Italy;1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;2. School of Mathematical Sciences, Peking University, 100871, Beijing, China;1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, ?itná 25, CZ-115 67 Praha 1, Czech Republic;2. Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany;3. Université de Toulon, IMATH, EA 2134, BP 20132, 83957 La Garde, France;1. Instituto de Matemática, Universidade Federal de Alagoas, Av. Lourival Melo Mota s/n, 57072-900, Maceió, Brazil;2. School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China;3. IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil
Abstract:We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense and which remain close to multi-solitons. We show that these solutions are necessarily pure multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization of multi-solitons and multi-breathers in terms of non dispersion.
Keywords:Generalized KdV equations  Solitons  Multi-solitons
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