Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities

Abstract: This work investigates the quadratic and quartic nonlinear diffusion–reaction equations with nonlinear convective flux terms, which are investigated analytically. Diffusion–reaction equations have a wide range of applications in several scientific areas, such as chemistry, biology, and population dynamics of the species. The new extended direct algebraic method is applied to obtain abundant families of solitary wave solutions. Different types of solitary wave solutions are obtained by applying this analytical method. This approach provides the solutions in the form of single and combined wave structures, which are observed in shock, complex solitary-shock, shock-singular, and periodic-singular forms. Some of the solutions are depicted graphically to illustrate the fact that they are, indeed, wave solutions of the mathematical model.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities ; volume:23 ; number:1 ; year:2025 ; extent:15 ; Open physics ; 23, Heft 1 (2025) (gesamt 15)

Contributors, Places and Time

• Creator: Ahmed, Nauman ; Macías-Díaz, Jorge E. ; Ali, Makhdoom ; Jawaz, Muhammad ; Baber, Muhammad Z. ; Medina-Guevara, María G.

Further information

• DOI: 10.1515/phys-2024-0115
• URN: urn:nbn:de:101:1-2502180253506.270144288740
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:29 AM CEST