İkinci mertebeden Benjamin-Ono denkleminin korunum kanunları yardımıyla çift indirgemesi ve tam çözümleri

Abstract

Bu çalışmada, ilk kez tabakalı sıvılardaki iç dalgaları tanımlamak için sunulan Benjamin-Ono denklemini ele alınmıştır. Lie nokta simetrileri ve yerel korunum vektörleri arasındaki ilişkiyi kullanarak hem değişken sayısında hem de denklemin mertebesinde bir indirgeme elde edilmiştir. İndirgenen denkleme yardımcı denklem metodu başarılı bir şekilde uygulanmş ve farklı tipte çözümler elde edilmiştir. Ayrıca çözümlerdeki parametrelerin özel değerleri için bazı grafik temsilleri verilmiştir.

Keywords

• Çift indirgeme yöntemi
• korunum vektörleri
• Benjamin-Ono denklemi

Double reduction of second order Benjamin-Ono equation via conservation laws and the exact solutions

Abstract

In this study, the Benjamin-Ono equation which was first introduced to describe internal waves in stratified fluids are considered. Using the association between Lie point symmetries and local conserved vectors, a reduction in both the number of variables and the order of the equation is achieved. The auxiliary equation method successfully applied to the reduced equation and different types of solutions are obtained. Moreover, some graphical representations for special values of the parameters in solutions are presented.

Keywords

• Double reduction method
• conservation vectors
• Benjamin-Ono equation

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