| Title: | NEW SOLITARY WAVE STRUCTURES IN TWO-DIMENSIONAL PERIODIC MEDIA |
| DOI No: | 10.1142/9789812770455_0014 |
| Source: | FRONTIERS OF APPLIED MATHEMATICS (pp 211-226)
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| Author(s): | ZUOQIANG SHI
Zhou Pei- Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China
JIANKE YANG
Permanent address: Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401, USA.
Zhou Pei- Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China
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| Abstract: | New solitary-wave structures in two-dimensional periodic media are obtained in the context of a two-dimensional nonlinear Schrödinger equation with a periodic potential. These new structures bifurcate from the edges of Bloch bands with two linearly independent Bloch modes. Away from these band edges, superposition of these Bloch modes, modulated by nonlinear effects, give rise to composite solitary waves with distinctive intensity and phase profiles such as vortex arrays. Using perturbation methods, coupled nonlinear envelope equations for the two Bloch waves near the band edges are analytically derived. Numerically, these composite solitons are directly computed both near and far away from the band edges, and the analytical results are fully confirmed. |
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