MANAS Journal of Engineering MJEN Volume 4 (Issue 1) (2016) Pages 52-62 MJEN MANAS Journal of Engineering, Volume 4 (Issue 1) © 2016 www.journals.manas.edu.kg The Tanh-Coth Method for Two System of Sobolev Type Equations In Mathematical Physics Şamil AKÇAĞIL Şeyh Edebali University, Faculty of Economics and Administrative Sciences, Bilecik, Turkey. samilakcagil@hotmail.com Ömer Faruk GÖZÜKIZIL Sakarya University, Department of Mathematics, Sakarya, Turkey. farukg@sakarya.edu.tr Received: 19.04.2016; Accepted: 06.05.2016 Abstract: Sobolev equations have been used to describe many physical phenomena and they are characterized by having mixed time and space derivatives appearing in the highest-order terms of an partial differential equation. In this work we consider two important system of Sobolev type equations namely improved Boussinesq and higher-order improved Boussinesq. By using tanh-coth method, we obtain abundant new travelling wave solutions of these important physical structures. Keywords: Sobolev equation; The tanh-coth method; The system of improved Boussinesq equations; The system of higher-order improved Boussinesq equations Matematiksel Fizikteki Sobolev Tipi İki Denklem Sistemi için Tanh-Coth Yöntemi Öz: Sobolov denklemleri en yüksek mertebeden türevinde zaman ve boyuta göre türevleri beraber bulunduran denklemler olarak tanımlanır. Bu çalışmada, Boussinesq ve yüksek mertebeden geliştirilmiş Boussinesq adlı iki önemli Sobolev denklem sistemini ele aldık. Tanh-coth yöntemi kullanarak bu iki önemli denklem sisteminin bir çok yeni hareketli dalga çözümünü elde ettik. Anahtar Kelimeler: Sobolev denklemi; Tanh-coth metot; Geliştirilmiş Boussinesq denklem sistemi; Yüksek mertebeden geliştirilmiş Boussinesq denklem sistemi.