You can buy external batteries of up to about 12,000 mAh. Pre-charge and use a USB lithium battery charger to charge your battery. Plus I'd carry several batteries.
That's kind of bulky but it'll work, and means you only have to bulk recharge occasionally.
Solar chargers might work if you get a good one--you'll need something with a high enough mAh output to charge reasonably during the day and a hookup that can mesh to your charger. I'd still carry a battery pack backup as the sun can be unreliable.
If you have a vehicle, an inverter to charge from your (running) engine will work as well. Even a small inverter will do very well as they tend to work in amps, not milliamps, and have no trouble running any battery charger. Inverters are available online, or from most auto shops, and tend not to be expensive. Personally, I'd buy a good one that does a sine wave output for a few more dollars--you can always use it to run a radio or light in the case of a power outage at home later.
