Multiple rational solutions for simplified modified Camassa–Holm dynamical model with applications in modern physics

This study provides a variety of lump, rational, breather solutions and stability analysis for the simplified modified Camassa–Holm equation (SMCHE). The ansatz transformations have been applied for finding multiple lump and breather solutions SMCHE. Lump, multi-wave, rogue wave, periodic wave, rational M-shaped solutions, periodic cross kink, periodic cross rational solitons, kink-cross rational solutions, homoclinic breathers, Akhmediev breather, generalized breather, and Kuznetsov–Ma breather solutions will all be evaluated, and their interactions with one another will be discussed. To further comprehend the physical phenomena of this equation, various 2D, 3D, and contour graphs are also constructed, and the stability of the governing equation is studied.