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G.L. Alfimov, E.V. Medvedeva, and D.E. Pelinovsky

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Wave systems with an infinite number of localized travelling waves

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Physical Review Letters 112, 054103 (2014) (5 pages)

**Abstract:**

In many wave systems, propagation of steadily travelling
solitons or kinks is prohibited because of resonances with linear
excitations. We show that wave systems with resonances may admit
an infinite number of travelling solitons or kinks if the closest to
the real axis singularities of a limiting
asymptotic solution in the complex upper half-plane are of the form
a+ib and a-ib. This quite a general statement is illustrated by
examples of the fifth-order Korteweg-de Vries-type equation, the
discrete cubic-quintic Klein-Gordon equation, and the nonlocal double
sine-Gordon equations.

**Keywords:**

Embedded solitons, bifurcations, beyond all orders, travelling kinks.