How to create a -15v rail from a +15v power supply
You can use an LM2596 in an inverting configuration.
According to Fig. 19, maximum load current should be around the 1A level.

There are probably some similar LTxxx products that are more expensive and better in this application. Initial start-up surge tends to be quite large in this configuration, hopefully your 4A capability will handle it.
Edit: For example, the LTC8364:

PCB layout and inductor specifications are quite important in a 2MHz converter so be careful to follow all the datasheet recommendations.