What qualifies as an example of love is a subjective topic, so please note that there are many examples that could correctly answer this question. That said, I will do my best to provide you with what I think are some strong examples to help get you started.
One prominent way that Allie and Noah show their love for each other is the way they express concern for one another’s well being. For example, consider how Noah encourages Allie to follow her own desires and goals instead of everyone else’s. This shows that he cares that she is happy.
Allie and Noah also show their love physically many times throughout the book. Consider the description of them laying by the fire:
They spent the day in each other’s arms ... holding each other ... sometimes he recited one of his favorite poems ...
In this scene we see that the pair provide compassionate, physical comfort to each other out of love. Noah’s recitations of his favorite poems also says a lot about their affection for one another. He’s not just reading anything to her, but poetry that means something to him because he wants to share beautiful things with her. This speaks volumes about how much they care for one another.
Another significant example of their love involves the letters. When Allie moved away, Nick sent her letters for a year and never heard back. The way he continued to write to her and express his love, even without a response, shows how devoted he was to her. His devotion is further seen in the way he works to refurbish the plantation where they had spent their summer exploring as teenagers. It’s almost as if the physical labor he put into restoring that land is a representation of the work he continued to put in their relationship.
Perhaps the most telling sign of their love is their continued devotion to each other as they grow old. In the beginning of the novel we see an older Noah reading to Allie at her bedside, even though she does not know who he is. The way he continues to care for her despite this drastic turn in their relationship shows how their love has stood the test of time.