I am assuming you are still maintaining your home in the USA as your official residence - you travel back and forth, but still come back to the same home.
As a USA citizen or resident, you are required to file a Federal income tax return and report all your worldwide income.
You may also be required to file a state income tax return if your home state imposes a state income tax.
For each of the international destinations that you are travelling to, you would need to research each country to see if it imposes a tax on foreigners working remotely from that country. If you have to pay any taxes on income that you earn while in a foreign country, you can claim a credit for the taxes paid to that foreign country on your USA tax return.
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