Kink and Periodic Waves in Nonlinear Shallow Water Models via IMSSEM and IGREMM
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Abstract
In this work, the simplified modified Camassa–Holm (smCH) equation, a reduced version of the original Camassa–Holm model, is employed to describe nonlinear wave behavior in shallow water and related physical systems, while preserving key nonlinear and dispersive effects. Two recently improved analytical methods, the improved modified Sardar sub-equation method (IMSSEM) and the improved generalized Riccati equation mapping method (IGREMM), are used to construct exact traveling-wave solutions of the smCH equation. These approaches yield various types of solutions expressed in exponential, trigonometric, and hyperbolic forms, capturing diverse nonlinear phenomena, including periodic and kink-type waves. Furthermore, the methodologies demonstrate strong potential for extension to other nonlinear partial differential equations, highlighting their versatility in analyzing complex wave dynamics.
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