Ajax Code:

$(function () {
    var $register = $(".register");
    var $login = $(".login");

    $login.find(".submit").on("click",function () {
        
    });

    $register.find("button").on("click", function(){
    //    ajax
        $.ajax({
            type:"post",
            url:"/api/user/register",
            data:{
                username: $register.find("[name="username"]").val(),
                password: $register.find("[name="password"]").val(),
                repassword: $register.find("[name="repassword"]").val(),
                email: $register.find("[name="email"]").val()
            },
            dataType:"json",
            success: function (result) {
                console.log(result);
            }
        });

    })
})

backend code:

/**
 * Created by Administrator on 2018/4/16.
 */

var express = require("express");
var router = express.Router();

//
var responseData;

router.use(function (req, res, next) {
    responseData = {
        code: 0,
        message:""
    }

    next();
});
/*
* 
* 
*
* 1.
* 2.
* 3.
* 
* 1.
*   
* */
router.post("/user/register", function (req, res, next) {
    var username = req.body.username;
    var password = req.body.password;
    var repassword = req.body.repassword;
    var email = req.body.email;
    console.log(username,password,repassword,email);

    //
    if(username == ""){
        responseData.code = 1;
        responseData.message = "";
        res.json(responseData);
        return;
    }
    //
    if(password == ""){
        responseData.code = 2;
        responseData.message = "";
        res.json(responseData);
        return;
    }
    //   
    if(password != repassword){
        responseData.code = 3;
        responseData.message = "";
        res.json(responseData);
        return;
    }
    responseData.message = "";
    res.json(responseData);
});

module.exports = router;

app.js:

/**
 * Created by Administrator on 2018/4/16.
 * 
 */
//express
var express = require("express");
//
var swig = require("swig");
//
var mongoose = require("mongoose");
//body-parserpost
var bodyParser = require("body-parser");
//app=>NodeHS Http.createServer()
var app = express();

//
//url/public__dirname + "/public"
app.use("/public", express.static(__dirname + "/public"));
// app.use("/static", express.static("public"));

//
//
//
app.engine("html", swig.renderFile);
//views
app.set("views", "./views");
/*view engineapp.engine*/
app.set("view engine", "html");
//
swig.setDefaults({cache: false});

//bodyparser
app.use( bodyParser.urlencoded({extended:true}) );

/*
 * 
 * */
app.use("/admin", require("./routers/admin"));
app.use("/api", require("./routers/api"));
app.use("/", require("./routers/main"));

//http
mongoose.connect("mongodb://localhost:27017/blog",function (err) {
    if(err){
        console.log("");
    }else{
        console.log("");
        app.listen(8081);
    }
});

HTML Code:

<form method="post" action="" class="register">
                <div class="inset-register">
                    <label for="username">:</label><input type="text" id="username" name="username">
                </div>
                <div class="inset-register">
                    <label for="password">:</label><input type="password" id="password" name="password">
                </div>
                <div class="inset-register">
                    <label for="repassword">:</label><input type="password" id="repassword" name="repassword">
                </div>
                <div class="inset-register">
                    <label for="email">:</label><input type="email" id="email" name="email">
                </div>
                <div class="inset-register">
                    <button ></button>
                </div>
            </form>

error reporting problem: