GENELLEŞTİRİLMİŞ ELASTİK ORTAMDAKİ YÜKSEK MERTEBE UZUN BOYUNA DALGA VE KISA BOYUNA DALGA DENKLEMLERİ
Bu çalışmada, genelleştirilmiş bir kübik elastik ortamda yayılan uzun ve kısa boyuna dalgalar arasındaki etkileşime yüksek mertebe doğrusal olmayan ve dispersif etkilerin katkısı incelenmiştir. Bu amaçla, ilk olarak, yüksek mertebe doğrusal olmayan ve dispersif etkileri içeren kısa boyuna dalganın evrimini tanımlayan yüksek mertebe nonlineer Schrödinger denklemi indirgeyici pertürbasyon yöntemi kullanılarak türetildi. Daha sonra, uzun boyuna dalganın faz hızının kısa boyuna dalganın grup hızına eşit olduğu durumlarda etkileşimin tanımlanması için yüksek mertebeden uzun boyuna dalga ve kısa boyuna dalga denklemleri bulundu. Buna ek olarak, Jacobi eliptik fonksiyon açılımı yöntemi, etkileşim denklemlerinin özel çözümlerini sunmak için kullanıldı.
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