A 3-5 hours battery life isnt SO bad. I mean, if you're playing in a car, you can use a car charger. If you're at home, just plug it in for a bit every few hours. If you're on a long train ride, they usually have outlets. The only instance where the battery life seems to be a problem if on a plane. But having that small battery add changes the whole story. Its small, and gives the system 9-15 hours. My 3DS gets the same battery life, and I have never had a problem
Solar panels for handheld devices are much much cheaper than the ones you get for home.
That said, this technology has been used for decades on cheap calculators ($5 tops).
Power Consumption of Cheap Calculator < Power Consumption of PSVita
My cheap Scientific Calculator (a generic Aurora) draws 20mA at 3V, according to a sticker on it. A small solar cell would suffice. However, for the vita you need 5V at high current (I would call 1A the minimum current to charge the battery at a steady pace). So, what if you take out the back touch panel and replace it with a solar panel? How long would it charge?
Well, this solar panel pumps out 5V at 130mA. That power rating is on the optimistic conditions, you are talking about bright sunny midday sunlight with no clouds and you are close to the equator and the panel is not overheating.
Now, the PSVita has a 2200mAh battery. Assuming a realistic charging efficiency of 60% and the Vita is fully off, it would take 24 hours of constant super super bright bright midday sun with no clouds and the light output of the sun remains constant. Seriously.
TLR, PSVita is impractical to have Solar Panel on, just get external battery pack.