(3+1)-Boyutlu Khokhlov–Zabolotskaya–Kuznetsov Denkleminin (G^'/G,1/G)-Açılım Metodu Yardımıyla Solitary Dalga Çözümleri

Year 2021, Volume 11, Issue 2, 290 - 301, 31.12.2021

Hülya DURUR Serbay DURAN Asıf YOKUŞ

https://doi.org/10.37094/adyujsci.885861

Abstract

Bu çalışmada, fiziksel olarak önemli bir yere sahip olan ses ışını (sound beam) olayına ışık tutan, özellikle lineer olmayan ortamda dağılım ve soğurma olmayan durumların matematiksel modeli olan (3+1)-boyutlu Khokhlov–Zabolotskaya–Kuznetsov (KZK) denklemi incelendi. Bu denklemin tam çözümünü bulmak için analitik metotlar arasında yer alan etkili ve güvenilir bir yöntem olan (G^'/G,1/G)-açılım metodu kullanıldı. Bu metodun seçilme amacı λ parametresinin durumlarına bağlı olarak birden fazla yürüyen dalga çözüm sınıfları elde edilmesidir. Bu sınıflar hiperbolik, trigonometrik, kompleks trigonometrik ve rasyonel formda kategorize edilir. Başarılı bir şekilde elde edilen bu çözüm sınıflarının temsil ettiği solitary dalgaların grafikleri 2-boyutlu, 3-boyutlu ve kontur olarak sunuldu. Bu makalede karmaşık aritmetik işlemler ve grafik çizimleri için hazır paket programlardan faydalanıldı.

Keywords

(G^, 1/G)-açılım metodu; (3+1)-boyutlu Khokhlov–Zabolotskaya–Kuznetsov Denklemi; Solitary dalga çözümleri.

Solitary Wave Solutions of the (3+1)-dimensional Khokhlov–Zabolotskaya–Kuznetsov Equation by Using the (G^'/G,1/G)-Expansion Method

Abstract

In this study, the (3+1)-dimensional Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, which is a mathematical model of non-absorption and dispersion in the non-linear medium, which sheds light on the sound beam phenomenon, which has a physically important place, is examined. In order to find the exact solution of this equation, an effective and reliable method, (G^'/G,1/G)-expansion method, is used among analytical methods. The purpose of this method is to obtain more than one traveling wave solution classes depending on the conditions of the λ parameter. These classes are categorized into hyperbolic, trigonometric, complex trigonometric and rational forms. The graphics of the solitary waves represented by these successfully obtained solution classes are presented as 2-dimensional, 3-dimensional and contours. This article makes use of ready-made package programs for complex arithmetic operations and graphic drawings.

Keywords

(G'/G,1/G)-Expansion Method, The (3+1)-dimensional Khokhlov–Zabolotskaya–Kuznetsov Equation, Traveling wave solution

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