You have to pass the query string through controller to view, and append the query string.
controller:
$params = array('psch' => $dogsearch, 'aval' => $aval);
params passed with a with statement to view:
->with('params', $params);
In view:
echo '<td>' . $dogs->appends($params)->links() . '</td>';
Just convert to blade if needed, I think:
{{ $dogs->appends($params)->links() }}
If only parameters, you have to pass each time through the route, and the query string will just hold the page number.
site/myparam1/myparam2?page=2
Parameters passed via route ARE NOT the same as query string parameters.
querystring
site/whatever?avar=hello&bvar=world&page=2
NOT querystring
site/whatever/hello/world?page=2
Before proceeding you may want to study up on difference in parameters and query string usage in laravel or just in general.
Just a suggestion.