On weak compactons to the nonlinearly dispersive mK(m, n, a, b) equation

In this paper, we investigated the precise existence conditions for weak compacton solutions of the nonlinearly dispersive mK(m, n, a, b) equation. By employing cutoff conditions, we derived a complete classification of parameters for compacton solutions. Specifically, Theorem 3.1 established four sets of sufficient conditions (Rt1–Rt4) under which a traveling wave solution possessed compact support. For the special parameters $a=b-1$, $m=1$, and $n=2b$, we derived the corresponding traveling wave ordinary differential equation and present explicit conserved integrals for mass, momentum, and energy. Furthermore, in Theorem 4.1, we provided general quadrature formulae for the compacton solutions. The results extend other studies on the mK(m, n, a, b) systems and offer an analytical framework for compacton existence in nonlinear dispersive equations.