How to use XPath on xml docs having default namespace

The XPath processing for a document that uses the default namespace (no prefix) is the same as the XPath processing for a document that uses prefixes:

For namespace qualified documents you can use a NamespaceContext when you execute the XPath. You will need to prefix the fragments in the XPath to match the NamespaceContext. The prefixes you use do not need to match the prefixes used in the document.

• http://download.oracle.com/javase/6/docs/api/javax/xml/namespace/NamespaceContext.html

Here is how it looks with your code:

import java.util.Iterator;
import javax.xml.namespace.NamespaceContext;
import javax.xml.parsers.DocumentBuilder;
import javax.xml.parsers.DocumentBuilderFactory;
import javax.xml.xpath.XPath;
import javax.xml.xpath.XPathConstants;
import javax.xml.xpath.XPathFactory;
import org.w3c.dom.Document;
import org.w3c.dom.NodeList;

public class Demo {

    public static void main(String[] args) {
        DocumentBuilderFactory domFactory = DocumentBuilderFactory.newInstance();
        domFactory.setNamespaceAware(true);
        try {
            DocumentBuilder builder = domFactory.newDocumentBuilder();
            Document dDoc = builder.parse("E:/test.xml");

            XPath xPath = XPathFactory.newInstance().newXPath();
            xPath.setNamespaceContext(new MyNamespaceContext());
            NodeList nl = (NodeList) xPath.evaluate("/ns:root/ns:author", dDoc, XPathConstants.NODESET);
            System.out.println(nl.getLength());
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private static class MyNamespaceContext implements NamespaceContext {

        public String getNamespaceURI(String prefix) {
            if("ns".equals(prefix)) {
                return "http://www.mydomain.com/schema";
            }
            return null;
        }

        public String getPrefix(String namespaceURI) {
            return null;
        }

        public Iterator getPrefixes(String namespaceURI) {
            return null;
        }

    }

}

Note:
I also used the corrected XPath suggested by Dennis.

The following also appears to work, and is closer to your original question:

import javax.xml.parsers.DocumentBuilder;
import javax.xml.parsers.DocumentBuilderFactory;
import javax.xml.xpath.XPath;
import javax.xml.xpath.XPathConstants;
import javax.xml.xpath.XPathFactory;

import org.w3c.dom.Document;
import org.w3c.dom.NodeList;

public class Demo {

    public static void main(String[] args) {
        DocumentBuilderFactory domFactory = DocumentBuilderFactory.newInstance();
        try {
            DocumentBuilder builder = domFactory.newDocumentBuilder();
            Document dDoc = builder.parse("E:/test.xml");

            XPath xPath = XPathFactory.newInstance().newXPath();
            NodeList nl = (NodeList) xPath.evaluate("/root/author", dDoc, XPathConstants.NODESET);
            System.out.println(nl.getLength());
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

}