Generalized Sub-Equation Method for the (1+1)-Dimensional Resonant Nonlinear Schrodinger’s Equation

Öz

Interest in studying nonlinear models has been increasing in recent years. Dynamical systems, in which the state of the system changes continuously over time, have nonlinear interactions. The use of unique nonlinear differential equations is inescapable in the evaluation of such systems. In mathematical point of view, for obtaining analytical solutions of nonlinear differential equations, it must be fully integrable. Consequently, the importance of fully integrable nonlinear differential equations for nonlinear science has become indisputable. Among these equations, one of the most studied by physicists and mathematicians is the nonlinear Schrödinger equation. This equation has undergone many modifications to evaluate different phenomena. In this study, the resonant nonlinear Schrödinger equation, which is the most important of these physical equations in terms of explaining many physical phenomena, is solved analytically with the generalized sub-equation method.

Anahtar Kelimeler

• Generalized Sub-Equation Method
• (1+1)-Dimensional Resonant Nonlinear Schrodinger’s Equation
• Exact Solution

(1+1)-Boyutlu Rezonant Doğrusal Olmayan Schrödinger Denklemi İçin Genelleştirilmiş Alt Denklem Yöntemi

Öz

Doğrusal olmayan modelleri incelemeye olan ilgi son yıllarda artmaktadır. Sistemin durumunun zaman içinde sürekli olarak değiştiği dinamik sistemler doğrusal olmayan etkileşimlere sahiptir. Bu tür sistemlerin değerlendirilmesinde benzersiz doğrusal olmayan diferansiyel denklemlerin kullanılması kaçınılmazdır. Matematiksel bakış açısına göre, doğrusal olmayan diferansiyel denklemlerin analitik çözümlerini elde etmek için, tamamen integre edilebilir olmalıdır. Sonuç olarak, doğrusal olmayan bilim için tamamen integre edilebilir doğrusal olmayan diferansiyel denklemlerin önemi tartışılmaz hale gelmiştir. Bu denklemler arasında fizikçiler ve matematikçiler tarafından en çok çalışılanlardan biri doğrusal olmayan Schrödinger denklemidir. Bu denklem, farklı olayları değerlendirmek için birçok değişikliğe uğramıştır. Bu çalışmada birçok fiziksel olguyu açıklama açısından bu fiziksel denklemlerin en önemlisi olan rezonans doğrusal olmayan Schrödinger denklemi genelleştirilmiş alt denklem yöntemi ile analitik olarak çözülmüştür.

Anahtar Kelimeler

• Genelleştirilmiş Alt Denklem Yöntemi
• (1+1) Boyutlu Resonant Doğrusal Olmayan Schrödinger Denklemi
• Tam Çözüm

Kaynakça

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