ReactJS: Redirect after form submit without refresh

Question

i have created a form which calls the search function after pressing submit button. I want the results of the search to be displayed in another function component (have used React Context for this purpose).

However, i faced an issue where i cannot link it to another route /yourstage/results WITHOUT refreshing the page. If the page is refreshed, my seachResult stored in state will be gone.

import React, { Fragment, useState, useEffect, useContext } from "react";
import { withRouter, Link } from "react-router-dom";
import searchResultContext from "./SearchResultContext";

const Search = () => {
  const [wave, setWave] = useState("$perc");
  const [pack_hu, setPackHu] = useState("$perc");
  const { searchResult, setSearchResult } = useContext(searchResultContext);

  useEffect(() => {
    console.log(JSON.stringify(searchResult));
  }, [searchResult]);

  //submit a form to search
  const submitSearch = async (e) => {
    e.preventDefault()
    try {
      const response = await fetch(
        `http://localhost:5000/yourstage/search/${wave}/${pack_hu}`,
        {
          method: "GET",
          headers: { "Content-Type": "application/json" },
        }
      );
      setSearchResult(await response.json());

      //Reset Form and State
      document.getElementById("searchForm").reset();
      setWave("$perc");
      setPackHu("$perc");

    } catch (error) {
      console.error(error.message);
    }
  };

  //return the form html
  return (
    <Fragment>
      <h1 className="text-center mt-3">Search</h1>
      <form id="searchForm" onSubmit={submitSearch}>
        <div className="form-group row">
          <label htmlFor="Wave" className="col-sm-2 col-form-label">
            Wave:
          </label>
          <div className="col-sm-10">
            <input
              type="text"
              className="form-control"
              placeholder="Wave Number"
              maxLength="10"
              onChange={(e) => setWave(e.target.value)}
            />
          </div>
        </div>

        <div className="form-group row">
          <label htmlFor="pack_hu" className="col-sm-2 col-form-label">
            Pack HU:
          </label>
          <div className="col-sm-10">
            <input
              type="text"
              className="form-control"
              placeholder="Pack HU"
              maxLength="10"
              onChange={(e) => setPackHu(e.target.value)}
            />
          </div>
        </div>

        <div className="row text-center mt-5">

          {/**Search based on parameter*/}
          <div className="col-6">
            <button type="submit" className="btn-lg btn-primary">
              <Link to="/yourstage/results">Search</Link>
            </button>
            
          </div>
        </div>
      </form>
    </Fragment>
  );
};

export default withRouter(Search);