Traveling wave solutions of degenerate coupled multi-KdV equations (Q2832735)

The authors consider the, so called, degenerate coupled \(\ell\)-Korteweg-de Vries equations. When traveling wave solutions are studied, the determination of their profiles reduces to an equation of the form \((f')^2=P(f)\) with a polynomial of degree \(\ell+2\). Two methods are proposed to solve that reduced O.D.E. One of them is related to the Chebyshev theorem on integrability of irrational functions. The second is based on the factorization of the polynomial \(P\). In particular, for \(\ell=3\), the authors derive solitary wave, kink-type and periodic solutions.