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. 2018 Mar 5;376(2117):20170183. doi: 10.1098/rsta.2017.0183

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© 2018 The Author(s)

Published by the Royal Society. All rights reserved.

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Figure 5. — (a) Numerically obtained evolution of the U₁-component of (3.12) with , G₁(U₂)=U₂+1, G₂(U₁)=U₁+2, (3.21) and ε=0.1. We observe that the profile—as expected since —blows-up, see also remark 2.2. (b) Numerically obtained evolution of the U₁-component for the same system and with the same initial condition, except that . The added small nonlinearity to G₁ prevents the profile from blowing-up (while it does not alter the leading order asymptotic results) and we observe the evolution of the profile to a breathing pinned 1-pulse solution. (Online version in colour.)

Inline graphic — (a) Numerically obtained evolution of the U₁-component of (3.12) with , G₁(U₂)=U₂+1, G₂(U₁)=U₁+2, (3.21) and ε=0.1. We observe that the profile—as expected since —blows-up, see also remark 2.2. (b) Numerically obtained evolution of the U₁-component for the same system and with the same initial condition, except that . The added small nonlinearity to G₁ prevents the profile from blowing-up (while it does not alter the leading order asymptotic results) and we observe the evolution of the profile to a breathing pinned 1-pulse solution. (Online version in colour.)