how to modify url without reloading page?

Yes, you can change url of browser without loading the web page using javascript window.history.pushstate, here is a example code which can help you

function AjaxSuccess(response, newUrl){
     document.getElementById("BodyContent").innerHTML = response.html;
     document.title = response.pageTitle;
     window.history.pushState({"html":response.html,"pageTitle":response.pageTitle},"", newUrl);
 }

In html5 new methods were introduced and you can use history.replaceState() and history.pushState() to change url of web browser without loading it, as these methods allow your to modify history of web browser

Read this article for more details of changing browser history

Yes, You can change history/URL of web browser without reloading it, your problem can be solved by implementing the History API, by using history.pushState() as mentioned in above answer

history.pushState('', 'Page Title', newURL);

check this working example here

hope this helps, thanks

Using HTML5  history.pushState() and history.replaceState() methods, which allow you to add and modify history entries, respectively.

window.history.pushState('newpage', 'Title', '/newpage.html');

Using pushState() changes the referrer that gets used in the HTTP header for XMLHttpRequest objects created after you change the state.

history.replaceState() operates exactly like history.pushState(), except that replaceState() modifies the current history entry instead of creating a new one.