Qualitative Study of Solitary Wave Profiles in a Dissipative Nonlinear Model

Beenish () and Fehaid Salem Alshammari
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Beenish: Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan
Fehaid Salem Alshammari: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia

Mathematics, 2025, vol. 13, issue 17, 1-17

Abstract: The convective Cahn–Hilliard–Oono equation is analyzed under the conditions μ 1 ≥ 0 and μ 3 + μ 4 ≤ 0 . The Lie invariance criteria are examined through symmetry generators, leading to the identification of Lie algebra, where translation symmetries exist in both space and time variables. By employing Lie group methods, the equation is transformed into a system of highly nonlinear ordinary differential equations using appropriate similarity transformations. The extended direct algebraic method are utilized to derive various soliton solutions, including kink, anti-kink, singular soliton, bright, dark, periodic, mixed periodic, mixed trigonometric, trigonometric, peakon soliton, anti-peaked with decay, shock, mixed shock-singular, mixed singular, complex solitary shock, singular, and shock wave solutions. The characteristics of selected solutions are illustrated in 3D, 2D, and contour plots for specific wave number effects. Additionally, the model’s stability is examined. These results contribute to advancing research by deepening the understanding of nonlinear wave structures and broadening the scope of knowledge in the field.

Keywords: group analysis; stability analysis; soliton solution; extended direct algebraic method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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