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Dispersive blow-up for solutions of the Zakharov-Kuznetsov equation
Authors:F. Linares  A. Pastor  J. Drumond Silva
Affiliation:1. IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, RJ, Brazil;2. IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, 13083-859, Campinas-SP, Brazil;3. Center for Mathematical Analysis, Geometry and Dynamical Systems, Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;1. EPFL SB, Station 8, CH-1015 Lausanne, Switzerland;2. Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland;3. IMATI-CNR, via Ferrata 5, I-27100 Pavia, Italy;1. Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA;2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John''s, NL A1C 5S7, Canada;3. Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA;4. Department of Mathematics, University of Missouri, Columbia, MO 65211, USA;5. Department of Mathematics, Miami University, Oxford, OH 45056, USA;1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil;2. Dipartimento di Matematica, Politecnico di Milano, Italy;1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, People''s Republic of China;2. Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, Republic of China;3. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, People''s Republic of China
Abstract:The main purpose here is the study of dispersive blow-up for solutions of the Zakharov-Kuznetsov equation. Dispersive blow-up refers to point singularities due to the focusing of short or long waves. We will construct initial data such that solutions of the linear problem present this kind of singularities. Then we show that the corresponding solutions of the nonlinear problem present dispersive blow-up inherited from the linear component part of the equation. Similar results are obtained for the generalized Zakharov-Kuznetsov equation.
Keywords:Nonlinear dispersive equations  Zakharov-Kuznetsov equation  Dispersive blow-up
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