A Numerical Study on the Stability of Solitary Wave Solutions of the Coupled Improved Boussinesq Equations

Öz

In this study, the time evolution of solitary wave solutions to the coupled improved Boussinesq equations, and their stability properties under small perturbations are numerically investigated. Examining the long-term behavior of solitary waves is of great importance for understanding nonlinear wave dynamics. For this purpose, the dynamics of solitary wave solutions are examined using a numerical scheme that combines the Fourier pseudo-spectral method for spatial discritization and the fourth-order Runge–Kutta method for time discritization. Several numerical experiments are carried out to demonstrate the accuracy and efficiency of the proposed method in both time and space. The long-time behavior of the waves with initially applied small perturbations is observed, and their stability is examined. The obtained results indicate that the solitary wave solutions of the coupled improved Boussinesq equations are stable under small perturbations.

Anahtar Kelimeler

• Coupled improved Boussinesq equations
• Time evolution
• Stability

Kuple Düzgünleştirilmiş Boussinesq Denklemlerinin Yalnız Dalga Çözümlerinin Kararlılığı Üzerine Sayısal Bir Çalışma

Öz

Bu çalışmada, kuple düzgünleştirilmiş Boussinesq denklemleri için yalnız (soliter) dalga çözümlerinin zaman evrimi ve küçük pertürbasyonlar altındaki kararlılık özellikleri sayısal olarak incelenmiştir. Yalnız dalgaların uzun zaman davranışlarını incelemek, doğrusal olmayan dalga dinamiklerini anlamak bakımından büyük önem taşımaktadır. Bu amaçla, uzay ayrıklaştırması için Fourier sözde (psödo)-spektral yöntemi ve zaman ayrıklaştırması için dördüncü mertebeden Runge-Kutta yöntemini birleştiren bir sayısal şema kullanılarak yalnız dalga çözümlerinin dinamikleri araştırılmıştır. Önerilen yöntemin hem zaman hem de uzaydaki doğruluğunu ve etkinliğini göstermek için çeşitli sayısal deneyler gerçekleştirilmiştir. Başlangıçta uygulanan küçük pertürbasyonlar ile dalgaların uzun zaman davranışları gözlemlenmiş ve kararlılıkları incelenmiştir. Elde edilen sonuçlar, kuple düzgünleştirilmiş Boussinesq denklemlerinin yalnız dalga çözümlerinin küçük pertürbasyonlar altında kararlı olduğunu göstermektedir.

Anahtar Kelimeler

• Kuple düzgünleştirilmiş Boussinesq denklemleri
• Zaman evrimi
• Kararlılık

Kaynakça

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