Traveling wave dynamics in higher-order nonlinear Klein–Gordon equations

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Yokus A., Isah M. A., Kaya D.

Ocean Engineering, cilt.356, sa.P1, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 356 Sayı: P1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.oceaneng.2026.125239
  • Dergi Adı: Ocean Engineering
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, Environment Index, Geobase, ICONDA Bibliographic, INSPEC, The International Construction Database (ICONDA), Academic Search Ultimate (EBSCO), Engineering Source (EBSCO)
  • Anahtar Kelimeler: Generalized Klein–Gordon equation, Jacobi elliptic functions, Kink soliton, Nonlinear evolution equations, Traveling wave solutions,
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

In this work, we investigate exact traveling wave solutions of higher-order generalized nonlinear Klein–Gordon equations using the ϕ6-expansion method. Such nonlinear partial differential equations arise in various physical contexts, including fluid dynamics, nonlinear optics, and quantum field theory. The study focuses on obtaining analytical solutions for specific cases with nonlinearity indices (Formula presented) and 5, corresponding to physically relevant scenarios. The solutions obtained are generated under specific constraint conditions derived from the parameter relationships and coefficient balance conditions that emerged during the application of the method. These constraints enable the fulfillment of reduced algebraic equations and guarantee the mathematical validity and physical applicability of the obtained wave solutions. Among these solutions, some solutions are expressed in terms of hyperbolic functions and exhibiting singularities at certain points represent wave structures that can be classified in the literature as singular hyperbolic traveling waves, trigonometric traveling waves, and singular periodic traveling wave solutions. Each solution is evaluated from a physical perspective, taking into account the relationships between the parameters in the model, and the behavior of the solution was examined for different values of the wave propagation parameter. The ϕ6-method enables the derivation of compactons, solitons, solitary wave patterns, and periodic waveforms in a straightforward and efficient manner. Comparisons with previous solution techniques, such as the tanh-function method and the (G′/G)-expansion method, highlight the efficiency and elegance of the proposed approach. The results contribute to the broader understanding of nonlinear wave phenomena and provide analytical tools for further applications in theoretical and applied physics.