Abundant different types of soliton solutions with stability analysis for the (2+1)-dimensional extended shallow water wave equation in ocean engineering with applications: Abundant different types of soliton solutions with stability

• Published in: Nonlinear dynamics 2025, Vol.113 (4), p.3713-3733
• Main Authors: Yousaf, Muhammad Zain, Abbas, Muhammad, Iqbal, Muhammad Kashif, Hamed, Y. S., Aljohani, A. F., Ahmad, Hijaz
• Format: Article
• Language: English
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Classical Mechanics; Control; Dynamical Systems; Physics; Physics and Astronomy; Statistical Physics and Dynamical Systems; Vibration
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-10372-w

The present study employs the improved F-expansion and modified exp ( - Z ( ς ) ) -expansion function methodologies to generate an enormous amount of novel wave solutions for the ( 2 + 1 ) -dimensional extended shallow water wave equation. This equation has widespread applications in many scientific and engineering domains, such as oceanography, hydraulic engineering, flood risk assessment, coastal engineering, tsunami modeling, environmental monitoring, and research on climate change. The improved F-expansion technique yields traveling wave solutions in the trigonometric and hyperbolic trigonometric formats while modified exp ( - Z ( ς ) ) -expansion function generates these solutions in the rational and linear forms in addition to trigonometric and hyperbolic trigonometric forms. In this regard, a wide range of solutions, which incorporate the kink pattern, Z-pattern, singular bell pattern or singular bright, anti-kink pattern, singular anti-bell pattern or singular dark, singular periodic pattern, singular pattern, singular complexiton pattern and plane pattern solitary wave solutions are generated via these two techniques. The physical significance of the solitons and singular solitons solutions that originated using these two analytical approaches are also discussed in this work. This work also discusses the stability analysis of the model. Applying the earlier described approach, provide a number of graphical representations, such as surface, 2 D , and contour graphics, that illustrate the computational and fluctuating characteristics of the produced solutions.