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

nonlinear engineering

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