Benney–Luke Denkleminde Doğrusal Olmayanlık ve Dağılımı Yakalamak için Modifiye Edilmiş Bir Genişleme Yaklaşımı

Abstract

Bu çalışma, sığ su dalga yayılımını modelleyen daha yüksek mertebeden bir dispersif model olan Benney–Luke denkleminin hareketli dalga çözümlerini incelemektedir. Açık biçimli analitik çözümler elde etmek için yardımcı fonksiyon yaklaşımı ile Jacobi eliptik fonksiyonlarını birleştiren değiştirilmiş bir genişletme yöntemi önerilmiştir. Elde edilen çözümler, parametrelere bağlı olarak çeşitli dalga formları göstermekte olup, doğrulukları sayısal simülasyonlarla desteklenmiştir. Sonuçlar, yöntemin doğrusal olmayanlık ve dispersiyon etkilerini başarıyla yakaladığını göstermektedir.

Keywords

• Benney-Luke Denklemi
• Seyreden Dalga Çözümleri
• Modifiye Genişleme
• Jacobi Eliptik Fonksiyonlar

A Modified Expansion Approach for Capturing Nonlinearity and Dispersion in the Benney–Luke Equation

Abstract

This study investigates traveling wave solutions of the Benney–Luke equation, a higher-order dispersive model for shallow-water wave propagation. A modified expansion method combining an auxiliary function approach with Jacobi elliptic functions is proposed to obtain explicit analytical solutions. The derived solutions exhibit various wave forms depending on key parameters, and their accuracy is supported by numerical simulations. The results confirm the method’s effectiveness in capturing nonlinear and dispersive effects in shallow-water wave dynamics.

Keywords

• Benney–Luke Equation
• Traveling Wave Solutions
• Modified Expansion Technique
• Jacobi Elliptic Functions

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