Boussinesq Denklemlerinin Hirota Direct Metod ile Tam Çözümleri

Yıl 2024, Cilt: 24 Sayı: 5, 1113 - 1119, 01.10.2024

Halide Gümüş , Abdullah Baykal

https://doi.org/10.35414/akufemubid.1404205

Öz

Boussinesq Denklemleri (BSQ) bu makalenin odak noktasıdır. İlk olarak, nonlineer evolüsyon denklemlere çoklu soliton çözümler oluşturmak için kullanılan Hirota'nın D operatörüne ilişkin temel bir genel bakış sunuyoruz. Daha sonra dördüncü dereceden BSQ ile ilgili bazı detaylar veriliyor ve bir soliton çözüm bulmak için Hirota Direct yöntemini kullanıyoruz. Hirota'nın bilineer yaklaşımı aynı zamanda nonlineer evolüsyon denklem olan altıncı dereceden Boussinesq benzeri denklem sınıfını çözmek için de kullanılır. Sonuçlar, bu yaklaşımın tam integre edilebilirlik gerektirdiğini doğrulamıştır.

Anahtar Kelimeler

Hirota Direct Metod, Boussinesq Denklemleri, Soliton çözümler, mathematica12

Exact Solutions of Boussinesq Equations By Hirota Direct Method

Öz

Boussinesq Equations (BSQ) are the focus of this article. First, we provide a basic overview of Hirota's D operator, which is used to build multi-soliton solutions for equations involving nonlinear evolution. After that, some details regarding fourth-order BSQ are provided, and we use Hirota's direct method to find a one-solution solution. Hirota's bilinear approach is also used to solve a class of sixth-order Boussinesq-like equations with nonlinear evolution. The outcomes verified that this approach requires complete integrability.

Anahtar Kelimeler

Hirota's Direct Method, Boussinesq equations, Soliton solutions, mathematica 12

Kaynakça

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