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|a Nixon, Sean D.
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|a Massachusetts Institute of Technology. Department of Mechanical Engineering
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|a Akylas, Triantaphyllos R.
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|a Yang, Jianke
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|a Akylas, Triantaphyllos R.
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|a Exponential Asymptotics for Line Solitons in Two-Dimensional Periodic Potentials
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|b Wiley Blackwell,
|c 2015-06-08T15:36:50Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/97216
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|a As a first step toward a fully two-dimensional asymptotic theory for the bifurcation of solitons from infinitesimal continuous waves, an analytical theory is presented for line solitons, whose envelope varies only along one direction, in general two-dimensional periodic potentials. For this two-dimensional problem, it is no longer viable to rely on a certain recurrence relation for going beyond all orders of the usual multiscale perturbation expansion, a key step of the exponential asymptotics procedure previously used for solitons in one-dimensional problems. Instead, we propose a more direct treatment which not only overcomes the recurrence-relation limitation, but also simplifies the exponential asymptotics process. Using this modified technique, we show that line solitons with any rational line slopes bifurcate out from every Bloch-band edge; and for each rational slope, two line-soliton families exist. Furthermore, line solitons can bifurcate from interior points of Bloch bands as well, but such line solitons exist only for a couple of special line angles due to resonance with the Bloch bands. In addition, we show that a countable set of multiline-soliton bound states can be constructed analytically. The analytical predictions are compared with numerical results for both symmetric and asymmetric potentials, and good agreement is obtained.
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|a United States. Air Force Office of Scientific Research (Grant USAF 9550-12-1-0244)
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|a en_US
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|a Article
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|t Studies in Applied Mathematics
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