Probing Novel Solitons and Travelling Wave Solutions of Nonlinear Evolution Equations in Mathematical Physics

ABSTRACT This work is concerned with the construction of the analytical travelling wave solutions for the ‐dimensional nonlinear compound KdV‐Burgers and the nonlinear KdV–Benjamin–Bona–Mahony–Burgers equations by means of a Riccati–Bernoulli subsidiary ordinary differential equation method. The implemented technique is observed to be an effective tool for addressing numerous higher‐order nonlinear evolution equations. Moreover, this technique can yield a novel infinite sequence of solutions by a Bäcklund transformation of the Riccati–Bernoulli equation. The obtained novel travelling wave solutions include solutions involving hyperbolic, trigonometric, and exponential functions. The resulting solutions are also compared with several analytical techniques, including the homogeneous balance method, the ‐expansion method, the improved trigonometric function method, the ‐expansion and the Kudryashov methods to demonstrate the reliability and efficiency of the implemented method. Finally, several two‐dimensional contour, density, and three‐dimensional graphical representations are depicted to illustrate the dynamics of the resulting travelling wave solutions.