Interactions of Parametrically Driven Dark Solitons. I: Néel-Néel and Bloch-Bloch interactions

Details Interactions of Parametrically Driven Dark Solitons. I: Néel-Néel and Bloch-Bloch interactions Interactions of Parametrically Driven Dark Solitons. I: Néel-Néel and Bloch-Bloch interactions

2006-12-27

arxiv.org/abs/nlin/0612059v2

Nonlinear Sciences

Pattern Formation and Solitons

46 pages, 23 figures. To appear in Phys Rev E. A reference added

Scientific paper

We study interactions between the dark solitons of the parametrically driven nonlinear Schr\"odinger equation, Eq.(\ref{NLS}). When the driving strength, $h$, is below $\sqrt{\gamma^2 +1/9}$, two well-separated N\'eel walls may repel or attract. They repel if their initial separation $2z(0)$ is larger than the distance $2z_u$ between the constituents in the unstable stationary complex of two walls. They attract and annihilate if $2z(0)$ is smaller than $2z_u$. Two N\'eel walls with $h$ lying between $\sqrt{\gamma^2 + 1/9}$ and a threshold driving strength $h_{sn}$ attract for $2z(0)<2z_u$ and evolve into a stable stationary bound state for $2z(0)>2z_u$. Finally, the N\'eel walls with $h$ greater than $h_{sn}$ attract and annihilate -- irrespective of their initial separation. Two Bloch walls of opposite chiralities attract, while Bloch walls of like chiralities repel -- except near the critical driving strength, where the difference between the like-handed and oppositely-handed walls becomes negligible. In this limit, similarly-handed walls at large separations repel while those placed at shorter distances may start moving in the same direction or transmute into an oppositely-handed pair and attract. The collision of two Bloch walls or two nondissipative N\'eel walls typically produces a quiescent or moving breather.

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