TY - JOUR T1 - ÖZEL BİR BAŞLANGIÇ KOŞULU ALTINDA (N+1) BOYUTLU BENJAMİN- ONO DENKLEMİ İÇİN WHITHAM MODÜLASYON TEORİSİ TT - WHITHAM MODULATION THEORY FOR (N+1) DIMENSIONAL BENJAMIN- ONO EQUATION WITH A SPECIAL INITIAL CONDITION AU - Demirci, Ali PY - 2019 DA - December Y2 - 2019 DO - 10.28948/ngumuh.632051 JF - Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi JO - NÖHÜ Müh. Bilim. Derg. PB - Nigde Omer Halisdemir University WT - DergiPark SN - 2564-6605 SP - 89 EP - 98 VL - 8 IS - 3 LA - tr AB - Buçalışmada, paraboloid tipi bir dalga cephesi boyunca uzanan basamak tipi birbaşlangıç koşulu için (n+1) boyutlu Benjamin- Ono denkleminin dispersif şokdalga çözümleri incelenmiştir. Bu amaçla, (n+1) boyutlu Benjamin- Ono denklemiuygun bir çözüm formu kullanılarak,(1+1) boyutlu değişken katsayılı Benjamin- Ono (nBO) tipi bir denkleme indirgenmiştir.nBO denkleminin dispersif şok dalgası çözümünü betimleyen Whitham modülasyondenklemleri uygun Riemann tipi değişkenler cinsinden türetilmiştir. Türetilenbu modülasyon denklemlerinin sayısal çözümlerinden elde edilen dispersif şokdalgası çözümleriyle, nBO denkleminin doğrudan sayısal çözümleri n=4 boyutuiçin karşılaştırılmış ve aralarında iyi bir uyumun olduğu görülmüştür. (n+1)boyutlu Benjamin- Ono denkleminin paraboloid tipi bir dalga cephesi boyuncayayılan dispersif şok dalgası çözümünün, indirgenmiş (1+1) boyutlu nBOdenkleminin dispersif şok dalgası çözümüyle betimlenebileceği gösterilmiştir. KW - Dispersif şok dalgaları KW - Whitham modülasyon teorisi KW - Benjamin- Ono denklemi N2 - Dispersive shockwaves (DSWs) in (n+1) dimensional Benjamin–Ono equation (nDBO) is consideredusing step like initial data along a paraboloid front. Employing a similarityreduction exactly reduces the study of such DSWs in (n + 1) dimensions to findingDSW solutions of (1+ 1) dimensional equations.With this ansatz, the nDBO equation can be exactly reduced to a Benjamin–Ono(nBO) type equation. Whitham modulation equations which describe DSW evolutionin the nBO equation are derived and Riemann type variables are introduced. DSWsobtained from the numerical solutions of the corresponding Whitham systems anddirect numerical simulations of the nBO equation are compared with very goodagreement obtained. It is concluded that the (n+1) DSW behavior along selfsimilar parabolic fronts can be effectively described by the DSW solutions ofthe reduced (1+ 1) dimensional equations. 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