GENELLEŞTİRİLMİŞ ELASTİK ORTAMDAKİ YÜKSEK MERTEBE UZUN BOYUNA DALGA VE KISA BOYUNA DALGA DENKLEMLERİ

Year 2019, Volume: 8 Issue: 3, 138 - 148, 20.12.2019

İrma Hacınlıyan

https://doi.org/10.28948/ngumuh.633157

Abstract

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.

Keywords

uzun dalga ve kısa dalga etkileşimleri, dalga yayılımı, tam çözümler, mikromorfik elastisite

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