Is it considered an act of disobedience for a sole son to travel seeking provision and securing his future and completing his marriage, if his elderly parents refuse to move and live with him?

If your parents need your service, do not travel without their permission. However, if they do not need you, or if there is someone else to serve them, there is no harm in your travel to complete your marriage and protect yourself [from sin], and this is not considered disobedience. Nevertheless, it is preferable to appease them and explain the benefits of your travel to them. Scholars have permitted a child to travel for seeking livelihood or knowledge without their parents' permission if the travel is safe and does not lead to neglecting them.

As for not living with them after marriage, there is no harm in it as long as it does not involve neglect or harm to them, especially if there are reasons for it, such as a cramped dwelling or the wife's desire for independence. Nevertheless, you must continue to honor them, be kind to them, and fulfill their needs, especially in their old age, as this is among the most obligatory duties.