Indian Military SAM Systems

Dual thrust literally means two thrust and is rather normal for such missiles.

Solid rocket fuels come in all different thrust levels and burn rates... thrust and burn rate are directly related so very high thrust means very high burn rate.

If you have room on your missile for 10kgs of rocket fuel, if you only use the highest thrust fastest burning fuel then your missile will be like a firework rocket... rapidly accelerate to top speed in 3 to 4 seconds and then burns out and just coasts as the speed bleeds off now the rocket motor is not operating.

The faster you move at low altitude the higher the drag so the faster you go the faster you slow down... using one thrust fuel is inefficient... like not having any gears in a car... just a direct drive transmission... so when you turn on your engine your wheels will spin.

Having dual thrust rocket fuel means you bake it like a cake... so the inner layer that burns first is high energy high thrust that burns very fast... this is good for getting the missile up and moving, so maybe enough for half a second burn... lets say with 10kgs of fuel space you get 5 seconds of burn time with the fastest burning fuel, so that would be 2kgs of fuel per second and half a second would be 1kg of fuel, so of the 10kgs of fuel 1kg is the high energy fastest burning fuel, the other 9kgs could burn at a slower rate but still be energetic... after the first kg of fuel has gotten you into the air the remaining 9kgs of fuel can generate less thrust but still accelerate the missile and allow it to climb and chase targets, but it burns at a quarter the speed of the fastest propellent, so instead of getting 4.5 seconds of thrust remaining as you would with the highest energy fuel you get 18 seconds...

Now this means your top speed wont be as high, but it massively increases your range and performance because a powered missile eliminates drag and allows it to accelerate in turns and fly much further than a missile which has burned out and is just coasting.

A very long range missile would use more high energy thrust fuel to climb and accelerate, but the lower thrust fuel will be much lower and essentially just a gas generator to blow some gas out the rear of the missile to counter drag and might burn for minutes rather than seconds... the higher and faster such weapons are released the greater their flight range... as shown by Kinzhal/Iskander.