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The present work aims at studying the dense gas of the molecular cloud LDN 1287 (L1287), which harbors a double FU Ori system, an energetic molecular outflow and a still-forming cluster of deeply embedded low-mass, young stellar objects, showing a high level of fragmentation. We present optical Halpha and [SII], and VLA NH$_3$ (1,1) and (2,2) observations with an angular resolution of ~3.5''. The observed NH$_3$ spectra have been analyzed with the HfS tool, fitting simultaneously three different velocity components. The NH$_3$ emission from L1287 comes from four different structures: a core associated with RNO 1, a guitar-shaped core (the "Guitar") and two interlaced filaments (the Blue and Red Filaments) roughly centered towards the binary FU Ori system RNO 1B/C and its associated cluster. Regarding the Guitar Core, there are clear signatures of gas infall onto a central mass that has been estimated to be ~2.1 $M_\odot$. Regarding the two filaments, they have radii ~0.03 pc, masses per unit length ~50 $M_\odot$ pc$^{-1}$, and are near isothermal equilibrium. A central cavity, probably related with the outflow, and also traced by the Halpha and [SII] emission, is identified, with several young stellar objects near its inner walls. Both filaments show clear signs of perturbation by the high-velocity gas of the outflows driven by one or several young stellar objects of the cluster. The Blue and Red filaments are coherent in velocity and have nearly subsonic gas motions, except at the position of the embedded sources. Velocity gradients across the Blue Filament can be interpreted either as infalling material onto the filament or rotation. Velocity gradients along the filaments are interpreted as infall motions towards a gravitational well at the intersection of both filaments.