As you all know IP indicates your location in the internet.
So where is 184.108.40.206 ?! According to cogents looking glass it's apparently less than a millisecond from london and less than 2 milliseconds from new york. But the minimum physically possible ping time between london and new york is around 37 milliseconds. What is going on?!
All the Internet really knows about a block of IP addresses is a series of possible routes for getting there. The routers pick one based on a set of critera and pass the packet along. So google advertise 220.127.116.11/24 from many locations around the world and then once it gets inside google's network it gets routed to a local DNS server cluster.
Similarly there would be nothing preventing an ISP advertising a block of addresses from many locations around the world and then routing either individual IPs or sub-blocks within their network to devices in many different locations around the world.
My question is, is there such a concept like a mobile router?
There are various things.
There are devices that route IP packets between stub networks and a cellular network, usually with NAT. Most smartphones offer the option of doing this and there are also dedicated devices for the task. These are what you will find if you google "mobile router". However such devices generally only have static routes or maybe a delegated IPv6 prefix, they don't get involved in routing protocols.
There has been a bunch of research on "mobile ad-hoc networks". That is building networks where a whole bunch of mobile devices work together to route data over longer distances than their individual radios can cover.
A dream of many anarchists has been to create an ad-hoc network that can connect people across a city without having to buy services from "the man" or build an organised hierarchy.
But scalability of such networks is a massive problem. As the number of nodes get higher routing overheads grow with them. As the area and hence the number of hops in the average communication grows the effective bandwidth available per user shrinks. Choosing the best route becomes a very hard problem. Reliability drops with hop count, especially if the routers are moving such that routing tables may be out of date by the time you get them.