Spatial solitons in double-well potentials. (English) Zbl 1534.35368
Summary: The existence, stability and propagation of spatial solitons in double-well potentials with cubic nonlinearity are investigated. The symmetric, tripole and quadrupole solitons show stability at lower power, while the symmetry-broken and antisymmetric solitons can remain stable throughout their existence curves. In comparison, the centered fundamental solitons are less stable than their symmetry-broken bound states and bifurcate from symmetric solitons. In this article, we study the effect of the separation between the two wells of the potential on the formation and stability of solitons. The threshold power of stable solitons tends to decrease with increasing separation for fundamental and symmetric solitons, while it is more complicated for tripole and quadrupole solitons. In general, there is a specific separation between two potential wells at which there are hardly any stable tripole and quadrupole solitons. Linear stability analysis and direct numerical simulations have provided evidence for the stability and propagation of solitons.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q51 | Soliton equations |
| 35C08 | Soliton solutions |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
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