Lineer olmayan adi diferansiyel denklemler için mevcut olan indirgeme metotlarından önemli iki tanesi λ-simetri ve Prelle-Singer metodudur. Bu metotlar aynı zamanda bahsi geçen denklemlerin ilk integrallerini ve integrasyon faktörlerini bulmak için oldukça elverişlidir. Bu çalışma Riemann sıfırlarının spektral realizasyonunu tanımlayan bir model olan özel bir Hamiltonian denklemine, bu metotların uygulanmasını sunmayı amaçlamaktadır. Ayrıca λ-simetri ve Prelle-Singer metotları arasındaki bağlantıya yer verilerek, bu ilişkinin sağladığı kolaylıklar detaylarıyla açıklanacak ve Hamiltonian denklemine uygulamaları birçok farklı durum için sunulacaktır.

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