The Destiny pulse weapons are early Ancient ship-to-ship weapons, several of which were installed on the starship Destiny and the Seed ship. The weapons are very similar to the much newer Lantean pulse weapons.
Destiny has double-barreled and triple-barreled turrets all along the hull, numbering at least in the dozens. They appear to be designed as anti-fighter weapons, able to fire rapidly and track fast moving targets. When activated, the double barreled weapons rise up from the hull and the turret pods open to reveal the weapons inside. The triple barreled turrets are always on the hull. On the underside of the hull is a large, four-barreled turret, which lowers away from the hull when activated. This weapon appears to be designed for attacking larger spacecraft such as motherships, as it has no apparent means of aiming horizontally and fires at a much slower rate. However, its shots are clearly superior to those of the double-barreled turrets, based on the effects it had on the shields of the Nakai mothership compared to the smaller turrets.
Due to the damage to the Destiny suffered during a previous attack, the current expedition was unable to activate the weapons safely. On Earth, scientists had believed they had found a way to get the expedition back home but it required the ship to enter into a star to refuel. To accomplish this, they attempted to and managed to use them in order to deplete the ships energy reserves which activated the Destiny's programming sending it to the nearest star in order to repower itself. (SGU: "Earth")
Later, during the alien attack on Destiny, the weapons were activated to fight the Nakai fighters and the Nakai mothership. Dr. Nicholas Rush had put a lockout in so that only 30% of the weapons could be activated at a time, but Eli Wallace managed to actviate the main forward battery as part of that. The weapons were used to destroy multiple enemy fighters and engage the mothership before it retreated, but firing the weapons drained power away from the shield and caused problems. Later, during the Mutiny on Destiny, Rush locked out the weapons completely and diverted all power to the shields as he believed that keeping the shields up for as long as possible was their only hope during the second alien attack. Eli managed to break the lockout, but ultimately agreed with Rush that firing the weapons was a bad idea and didn't use them. (SGU: "Space", "Divided")
Later, during the alien attack in the void, the weapons were put into use again to defend against the Nakai fighters, trying to keep them off the ship for as long as possible. While a few fighters were likely destroyed, there were too many to prevent all of them from reaching the ship, but Dr. Jeremy Franklin managed to use the Destiny interface chair to send Destiny back into FTL before the ship could be boarded, also destroying the fighters that were nearby trying to board. (SGU: "Sabotage")
During one of Colonel Everett Young's visions of Destiny being destroyed, his first attempt was to power the weapons but was soon overpowered by the alien fighters, with the ship being destroyed in the end. After his dream, during a morning briefing, Dr. Lisa Park was explaining the maintenance robot repairing the domed room to a larger hydroponics, Young instead wanted the weapon system repaired since they had about a half dozen gun batteries offline. (SGU: "Trial and Error")
During the Drone attack on Destiny, the weapons were used to defend the ship from Berzerker drones. Later, when the crew attacked the Control Ship, they managed to bring Destiny in close enough to use the main cannon and destroy the ship. (SGU: "Resurgence", "Deliverance")
When Destiny arrived at Novus, the crew were unable to break into the Novus fallout bunker with C-4 or the Ancient shuttle's weapons so the crew used a single shot from Destiny's main weapon fired at 40 percent power to blast a hole in the door. (SGU: "Epilogue")
When the crew attacked the drones, the anti-fighter turrets were called into use to defend the ship from the fighters before the main weapon was used to damage and later destroy the Control Ship. (SGU: "Gauntlet")