Explicit solutions and stability analysis of the (2 + 1) dimensional KP–BBM equation with dispersion effect

• A small dispersion effect is introduced to the (2 + 1)-dimensional KP–BBM equation.
• Dynamical system theory is applied to find bounded traveling wave solutions.
• General solutions are obtained in terms of elliptic functions.
• Technique based on factorization method and functional transformation is proposed.
• Stability analysis of the dispersive waves are examined.

This paper is devoted in the study of (2 + 1) dimensional KP–BBM equation. A small dispersion of waves is included and the nature of the solutions are examined under this effect using the theory of dynamical system. We prove that in the presence of dispersion effect on the equation, yet there exists bounded traveling wave solutions in different classes in terms of solitary waves, periodic and elliptic functions in certain regions. We obtain the general solution of the equation with or without the dispersion effect in terms of Weirstrass ℘℘ functions and Jacobi elliptic functions. A new technique based on the application of factorization method and the use of functional transformation yields new form of solutions. Finally, we discuss the stability analysis which shows that the traveling wave speed is a bifurcation parameter, which modulates between different classes of waves. Using phase plane analysis, we show that the solution has a transcritical bifurcation at a critical velocity.