this.router.navigate returns a promise so you can simply use:

this.router.navigate(["/search", "1", ""]).then(()=>{
  // do whatever you need after navigation succeeds
});

// In javascript
this.router.navigate(["/search", "1", ""])
    .then(succeeded => {
        if(succeeded)
        {
            // Do your stuff
        }
        else
        {
            // Do some other stuff
        }
    })
    .catch(error => {
        // Handle the error
    });

// In typescript you can use the javascript example as well.
// But you can also do:
try
{
    let succeeded = await this.router.navigate(["/search", "1", ""]);
    if(succeeded)
    {
        // Do your stuff
    }
    else
    {
        // Do some other stuff
    }
}
catch(error)
{
    // Handle the error
}

Not entirely sure of the context but an option would be to subscribe to a change in the URL using ActivatedRoute

https://angular.io/docs/ts/latest/guide/router.html#!#activated-route

Here's an example:

...
import { ActivatedRoute } from '@angular/router';
...

private _routerSubscription: any;

// Some class or service

constructor(private _route: ActivatedRoute){
    this._routerSubscription = this._route.url.subscribe(url => {
        // Your action/function will go here
    });
}

There are many other observables you can subscribe to in ActivatedRoute which are listed in that link if url isn't quite what you need.

The subscription can be done in the constructor() or in an ngOnInit() depending on what suits you best, just remember to clean up after yourself and unsubscribe in an ngOnDestroy() :)

this._routerSubscription.unsubscribe();