I applied custom master page for SharePoint enterprise search center site,I can't see the left side web parts like author and other refiners ,Is it possible to set a page layout for result page?
There is nothing "special" about the search pages. The web parts work on any page. You just have to configure them. If you have your own page layouts, just create new pages with your page layouts and use them. That means, of course, that your designers have to account for the layout of the search center pages.