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      Applying the New Extended Direct Algebraic Method to Solve the Equation of Obliquely Interacting Waves in Shallow Waters

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          Abstract

          In this study, the potential Kadomtsev-Petviashvili (pKP) equation, which describes the oblique interaction of surface waves in shallow waters, is solved by the new extended direct algebraic method. The results of the study show that by applying the new direct algebraic method to the pKP equation, the behavior of the obliquely interacting surface waves in two dimensions can be analyzed. This article fairly clarifies the behaviors of surface waves in shallow waters. In the literature, several mathematical models have been developed in attempt to study these behaviors, with nonlinear mathematics being one of the most important steps; however, the investigations are still at a level that can be called ‘baby steps’. Therefore, every study to be carried out in this context is of great importance. Thus, this study will serve as a reference to guide scientists working in this field.

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          Author and article information

          Journal
          JOUC
          Journal of Ocean University of China
          Science Press and Springer (China )
          1672-5182
          10 July 2020
          01 August 2020
          : 19
          : 4
          : 772-780
          Affiliations
          1Department of Mathematics, Faculty of Science and Art, Pamukkale University, Denizli 20160, Türkiye
          2Department of Physic, Faculty of Science and Art, Mustafa Kemal University, Hatay 31001, Türkiye
          3Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Hatay 31001, Türkiye
          Author notes
          *Corresponding author: KURT Ali, E-mail: akurt@ 123456pau.edu.tr
          Article
          s11802-020-4135-8
          10.1007/s11802-020-4135-8
          Copyright © Ocean University of China, Science Press and Springer-Verlag GmbH Germany 2020.

          The copyright to this article, including any graphic elements therein (e.g. illustrations, charts, moving images), is hereby assigned for good and valuable consideration to the editorial office of Journal of Ocean University of China, Science Press and Springer effective if and when the article is accepted for publication and to the extent assignable if assignability is restricted for by applicable law or regulations (e.g. for U.S. government or crown employees).

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          Self URI (journal-page): https://www.springer.com/journal/11802

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