Well, it's a tough situation. In a light novel, things might seem more dramatic, but in real life, you should assess your own feelings. If she cheated, it's a serious betrayal. You might want to distance yourself from her for a while to clear your head. Think about how important the relationship was to you before this happened. And also, don't blame yourself. It's her actions that are at fault.
Coping with the pain is not easy. First, accept that you're in pain. It's a normal reaction. Then, you could try new experiences. Go to new places, meet new people. It might open up new possibilities for you. Also, consider talking to a counselor or a therapist if the pain is too overwhelming. They are trained to help you deal with emotional distress and can offer useful advice on how to move forward.
It's possible, but it won't be easy. She has to be a very forgiving person. You need to be completely honest with her about what happened and why. Then, you need to be prepared to do whatever it takes to make it up to her. It could take a long time for her to trust you again, and she may always have some doubts in the back of her mind.
Another theme is self - discovery. As the story progresses, the characters learn more about themselves and their feelings. For example, the main character may find out things about his own capacity for love and commitment that he didn't know before. It's a journey of growing up in terms of emotions.
You're in a tough situation. Loving her doesn't excuse what you did. You need to show remorse. Maybe write her a letter explaining everything - how it happened, why it happened, and how much you regret it. And then, prove your love through actions. Be more attentive, more present in her life, and always be honest from now on. But don't be surprised if she doesn't want to forgive you right away or at all.
One similar novel could be 'My Youth Romantic Comedy Is Wrong, As I Expected'. It also has an English dub and features interesting character relationships and humorous dialogue.