Yerel ve Lineer olmayan Kuple Dalga Denklemlerinin Genel Sınıfı için Yalnız Dalga Çözümleri

Abstract

Bu makalede çekirdek fonksiyonları ile konvolüsyon işlemini içeren, yerel ve doğrusal olmayan kuple dalga denklemlerinin genel bir sınıfını inceliyoruz. Çekirdek fonksiyonlarının uygun seçimleri için sistem, Toda kafes sistemi, kuple Boussinesq denklemleri gibi iyi bilinen doğrusal olmayan kuple dalga denklemleri haline gelir. Petviashvili yöntemi kullanılarak, sistemin yalnız dalga çözümleri için bir sayısal şema önerilmiştir. Farklı çekirdekler kullanılarak, sayısal yöntemin geçerliliği test edilmiştir.

Keywords

• Kuple Boussinesq denklemler
• Petviashvili iterasyon yöntemi
• yalnız dalga çözümleri.

Solitary Wave Solutions to the General Class of Nonlocal Nonlinear Coupled Wave Equations

Abstract

In this paper, we study a general class of nonlocal nonlinear coupled wave equations that includes the convolution operation with kernel functions. For appropriate selections of the kernel functions, the system becomes well-known nonlinear coupled wave equations, for instance Toda lattice system, coupled improved Boussinesq equations. A numerical scheme is proposed for the solitary wave solutions of the system using the Pethiashvili method. Using the different kernels, the validity of the numerical method has been tested.

Keywords

• Coupled Boussinesq equations
• Petviashvili's iteration method
• solitary wave solutions.

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