Advanced Mathematical Models & Applications

ISSN Online: 2519-4445

Advanced Mathematical Models & Applications is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues.

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Analytical Structures and Conservation Laws of the (2+1)-Dimensional Cubic Klein-Gordon Equation

Esin İlhan

Published: 02-08-2026

https://doi.org/10.62476/amma112363

Abstract

The (2+1) cubic Klein-Gordon equation is used in a wide range of disciplines, including river floods, tsunami wave propagation, breakwater construction and management, dam-break scenarios, coastal engineering, and many phenomena in physical oceanography. The goal of this study is to establish wave solutions using the extended rational sine-cosine and sinh-cosh techniques (ERSC). The provided approaches enable the construction of a variety of novel solutions with distinct forms. The solutions are closely tied to physical characteristics, with particular waveform features that appear under certain conditions. Furthermore, the new conservation theorem is applied to systematically deduce conservation laws from Lie-point symmetry. Graphical representations in two- and three-dimensional formats are plotted to demonstrate the propagation of selected exact solutions that include a variety of parameter values.