Why is it not working?

I want to create a program that will transform the same words into one. I have a problem with code where I used "while". If I put "if" instead of "while" its working, but not as right as I want, so I need to use "while", but its not working correctly. Its compiling, but not working after inputting the string a.

#include <iostream>

using namespace std;

int main ( ) {
    string a;
    cout << "Введите string a: ";
    getline(cin,a);
    for (int i = 0; i < a.length(); i++) {
        while (a[i]=a[i+1]) {
            for (int z = i; z < a.length(); z++) {
                a[z]=a[z+1];
            }
        }
    }
    cout << endl << a << endl;
}