Investigation of traveling wave solutions of nonlinear mathematical models by the modified exponential function method

Abstract

In this work, traveling wave solutions of (1+1)-dimensional Landau-Ginzburg-Higgs and Duffing nonlinear partial differential equations, which are examples of mathematical modeling, are obtained and analyzed using the modified exponential function method. In order to facilitate the physical interpretation of the mathematical models represented by these equations, simulations of the behavior of the mathematical model as three-dimensional, contour, density and two-dimensional graphics are given using a package program with the help of appropriate parameters. It has been shown that the modified exponential function method effectively investigates the solutions of (1+1)-dimensional Landau-Ginzburg-Higgs and Duffing equations.

Keywords

• Traveling wave solutions
• (1+1)-dimensional landau-ginzburg-higgs equation
• duffing equation
• the modified exponential function method

Lineer olmayan matematiksel modellerin hareketli dalga çözümlerinin genişletilmiş üstel fonksiyon metodu kullanılarak incelenmesi

Abstract

Bu çalışmada, matematiksel modelleme örnekleri olan (1+1)-boyutlu Landau-Ginzburg-Higgs ve Duffing doğrusal olmayan kısmi diferansiyel denklemlerin yürüyen dalga çözümleri elde edilmiş ve genişletilmiş üstel fonksiyon metodu kullanılarak analiz edilmiştir. Bu denklemlerin temsil ettiği matematiksel modellerin fiziksel yorumunu kolaylaştırmak için uygun parametreler yardımıyla bir paket program kullanılarak matematiksel modelin davranışının üç boyutlu, kontur, yoğunluk ve iki boyutlu grafikleri olarak simülasyonları verilmiştir. Genişletilmiş üstel fonksiyon metodunun (1+1)-boyutlu Landau-Ginzburg-Higgs ve Duffing denklemlerinin çözümlerinin araştırılmasında etkili bir yöntem olduğu gösterilmiştir.

Keywords

• Yürüyen dalga çözümleri
• (1+1)-ölçülü landau-ginzburg-higgs denklemi
• duffing denklemi
• genişletilmiş üstel fonksiyon metodu

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