İntegrallenebilir denklemler için soliton çözümler ve uygulamaları
Küçük Resim Yok
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İstanbul Ticaret Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu çalışmada, Korteweg- de Vries-Burgers denkleminin ve genelleştirilmiş Kawahara denkleminin integrallenemez olduğu Painlevé testi kullanılarak gösterilmiştir. Her iki denklem için Painlevé analizinin yeni bir yaklaşımı, teorik olarak kurulmuştur. Daha sonra integrallenemez bir denklemin genel değil özel tam çözümünün olacağı belirtilmiştir. Denklemlerin tam çözümü ise Hirota metodu ve basitleştirilmiş Hirota metodu ile bulunmuştur.
In this study, by using Painlevé test, it is determined that the Korteweg- de Vries-Burgers' equation and generalized Kawahara equation are nonintegrable. Painlevé analysis was established as a new approach to both theoretical equations. Then, it is expressed that a nonintegrable equation has exact solution not general solution. As a final, the exact solutions of the equations are obtained by using a simplified Hirota method.
In this study, by using Painlevé test, it is determined that the Korteweg- de Vries-Burgers' equation and generalized Kawahara equation are nonintegrable. Painlevé analysis was established as a new approach to both theoretical equations. Then, it is expressed that a nonintegrable equation has exact solution not general solution. As a final, the exact solutions of the equations are obtained by using a simplified Hirota method.
Açıklama
Fen Bilimleri Enstitüsü, Matematik Ana Bilim Dalı
Anahtar Kelimeler
Matematik, Mathematics
