Doğrusal olmayan Bretherton denkleminin periyodik gezen dalga çözümleri

Abstract

Bu çalışmada, dördüncü dereceden doğrusal olmayan dalga denklemi olan doğrusal olmayan Bretherton denkleminin küresel periyodik ve üstel olarak büyüyen çözümlerinin kapalı formları ortaya çıkarılmıştır. Yarı-doğrusal Bretherton denklemi, kirişli ve kirişsiz asma köprülerdeki periyodik salınımları modellemek için yaygın olarak kullanılmaktadır. Bununla birlikte, bildiğimiz kadarıyla, Bretherton denkleminin doğrusal olmayan versiyonu literatürde ilk kez önerilmiştir. Sec-ansatz adı verilen bir yöntem kullanılarak elde edilen doğrusal olmayan Bretherton denkleminin tam çözümleri tartışılmış ve örneklerle gösterilmiştir.

Keywords

• Patlayan çözümler
• Bretherton denklemi
• Global çözümler
• Doğrusal olmama
• Gezen dalga çözümleri

Periodic travelling wave solutions of the nonlinear Bretherton equation

Abstract

In this study, the closed-forms of global periodic and exponentially growing unbounded solutions for the nonlinear Bretherton equation, which is the fourth-order nonlinear wave equation, are revealed. The semi-linear Bretherton equation is commonly used to model periodic oscillatory behavior in suspension bridges, both with and without girders. However, to our knowledge, the nonlinear version of the Bretherton equation is proposed for the first time in the literature. The exact solutions of the nonlinear Bretherton equation, obtained using a method called sec-ansatz, are discussed and illustrated with examples.

Keywords

• Blow-up solutions
• Bretherton equation
• Global solutions
• Nonlinearity
• Travelling wave solutions

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