Combine "Live search text field" to "Laravel form"

I have contact form and I add Live search item view script in it. Here is live search input area.

<div class="btn-group">
    <input type="text" name="search" id="search" 
placeholder="Please type item name or product number" class="form-control" 
size="3000" onkeypress="return event.keyCode!=13" />
     <span class="searchclear glyphicon glyphicon-remove-circle"></span>
</div>

And this is the based contact from script

           <div class="form-group">
                {!! Form::label('search', 'search:', ['class' => 'col-sm-2 control-label']) !!}

                <div class="col-sm-10">
                    {!! Form::text('search', null, ['class' => 'form-control']) !!}

                    @if ($errors->has('search'))
                        <span class="help-block">
                            <strong></strong>
                        </span>
                    @endif
                </div>
            </div>

I would like to fill in the live search data next page using "Laravel form" but it didn't work. Could someone teach me how to combine livesearch data section as Laravel Form please?

via Chebli Mohamed