New kink-periodic and convex–concave-periodic solutions to the modified regularized long wave equation by means of modified rational trigonometric–hyperbolic functions

Abstract The significance of different types periodic solutions in nonlinear equations is vital across various practical applications. Our objective this study was to uncover novel forms for the modified regularized long wave equation. This particular model holds great importance realm physics as it characterizes propagation weak nonlinearity and space-time dispersion waves, encompassing phenomena like transverse waves shallow water, ion-acoustic plasma, phonon crystals. By employing methodology rational sine-cosine sinh–cosh functions, we successfully derived new kink-periodic convex–concave-periodic solutions. To showcase superiority our proposed approach, conducted a comparative analysis with alternative Kudryashov-expansion technique. Furthermore, visually depicted diverse recovery through 2D 3D plots enhance understanding findings.