(1+1)-Boyutlu Van Der Waals Gaz Sistemi için Dalga Çözümlerinin Belirlenmesinde Abel Denklem Yöntemi

Öz

Bu çalışma, (1+1) boyutlu Van der Waals gaz sistemi için üstel yapılar içeren rasyonel biçimli çözümlerin türetilmesi ve sınıflandırılmasına adanmıştır. Analiz, uygun kısıtlar altında sabit katsayılı Abel denkleminin kapalı form çözümlerinin elde edilmesiyle başlamaktadır. Elde edilen bu çözümler, sonlu bir seri yaklaşımı çerçevesinde gaz sisteminin çözümünü ifade etmek için yapı taşları olarak kullanılmaktadır.Bu temsilin yönetici denklemlere yerleştirilmesiyle problem, birden fazla bilinmeyen parametre içeren doğrusal olmayan cebirsel bir sisteme indirgenmektedir. Söz konusu sistem, Mathematica yazılım paketinin yardımıyla sembolik olarak çözülmektedir. Bu sayede, doğrusal olmayan Van der Waals modeli için üstel-rasyonel ifadelerle karakterize edilen bir tam çözüm ailesi elde edilmektedir.Elde edilen sonuçların daha iyi yorumlanabilmesi amacıyla, türetilen dalga profillerinin dinamik davranışı; iki ve üç boyutlu grafikler ile kontur ve yoğunluk dağılımları kullanılarak incelenmektedir.

Anahtar Kelimeler

• sabit katsayılı Abel denklemi
• (1+1) boyutlu Van der Waals gaz sistemi
• Abel denklem yöntemi
• dalga çözümleri

Abel Equation Method for Determining the Wave Solutions of (1+1)-Dimensional Van Der Waals Gas System

Öz

This work is devoted to the derivation and classification of rational-form solutions containing exponential structures for the (1+1)-dimensional Van der Waals gas system. The analysis begins with the construction of closed-form solutions of the Abel equation with constant coefficients under suitable restrictions. These solutions are then employed as building blocks to represent the solution of the gas system through a finite series framework. By incorporating this representation into the governing equations, the problem is transformed into a nonlinear algebraic system involving several unknown parameters. This system is solved symbolically with the assistance of the Mathematica software package. Consequently, a family of exact solutions characterized by exponential-rational expressions is obtained for the nonlinear Van der Waals model. To further interpret the results, the dynamical behavior of the derived wave profiles is examined using graphical techniques, including two-dimensional and three-dimensional plots, as well as contour and density distributions.

Anahtar Kelimeler

• Abel equation with constant coefficient
• (1+1)-dimensional Van der Waals gas system
• Abel equation method
• wave solutions.

Etik Beyan

This study has been conducted in accordance with accepted ethical principles, and no ethical issues arise from its publication.

Teşekkür

This article is derived from Coşkun Atağ's doctoral thesis, supervised by Gürhan İçöz.

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