You can use the DataTables api to filter the table. So all you need is your own input field with a keyup event that triggers the filter function to DataTables. With css or jquery you can hide/remove the existing search input field. Or maybe DataTables has a setting to remove/not-include it.
Checkout the Datatables API documentation on this.
Example:
HTML
<input type="text" id="myInputTextField">
JS
oTable = $('#myTable').DataTable(); //pay attention to capital D, which is mandatory to retrieve "api" datatables' object, as @Lionel said
$('#myInputTextField').keyup(function(){
oTable.search($(this).val()).draw() ;
})
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