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Accumulation of embedded solitons in systems with quadratic nonlinearity

B. A. Malomed·T. Wagenknecht·A. R. Champneys·M. J. Pearce
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Abstract

Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multi-wave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero solution has a fourfold zero eigenvalue. In this paper, the existence of such solutions is studied in a three-wave model. An appropriate rescaling casts the system in a normal form, which is universal for models supporting ESs through quadratic nonlinearities. The normal-form system contains a single irreducible parameter $ε$, and is tantamount to the basic model of type-I second-harmonic generation. An analytical approximation of WKB type yields an asymptotic formula for the distribution of discrete values of $ε$ at which the ESs exist. Comparison with numerical results shows that the asymptotic formula yields an exact value of the scaling index, -6/5, and a fairly good approximation for the numerical factor in front of the scaling term.

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B. A. Malomed, T. Wagenknecht, A. R. Champneys, M. J. Pearce. 2005-05-04. Accumulation of embedded solitons in systems with quadratic nonlinearity. https://doi.org/10.1063/1.1938433

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