On shifted periodic solutions of two nonlinear equations |
| |
| Institution: | 1. Department of Physics, Duke University, Durham, North Carolina, USA;2. The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois, USA;3. Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois, USA;4. Canadian Neutron Beam Centre, Chalk River Laboratories, Chalk River, Ontario, Canada;5. Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada;6. Canadian Institute for Advanced Research, Toronto, Ontario, Canada;7. Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada;1. Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-4515, USA;2. Mathematical Institute, University of Oxford, Oxford, UK;3. Center for Biomedical Computing, Simula Research Laboratory, Oslo, Norway;2. SUPA, School of Physics and Astronomy, The University of Glasgow, Glasgow, United Kingdom |
| |
| Abstract: | Using the linear superposition approach, we find periodic solutions with shifted periods and velocities of the (2 + 1)-dimensional modified Zakharov–Kuznetsov equation and the (3 + 1)-dimensional Kadomtsev–Petviashvili equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure of generating solutions of nonlinear evolution equations is successful as a consequence of some cyclic identities satisfied by the Jacobi elliptic functions which reduce by 2 (or a larger even number) the degree of cyclic homogeneous polynomials in Jacobi elliptic functions. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
