Álvaro H. Salas

Painlev\'e Integrability, Hamiltonian Structure and Exact Elliptic Reductions of a Generalized Nonlinear Wave Equation

We study the polynomial generalized Korteweg--de Vries family \[ u_t+P_m(u)u_x+\kappa u_{xxx}=0,\qquad \kappa\neq0, \] where $P_m$ is a real polynomial of degree $m\ge1$. The purpose is not to generate isolated closed-form waves, but to identify the structural threshold at which pole-type Painlev\'e behavior and ellipt...