On classical solutions for the fifth‐order short pulse equation

Abstract

The fifth‐order short pulse equation models the nonlinear propagation of optical pulses of a few oscillations duration in dielectric media. In particular, it models the propagation of circularly and elliptically polarized few‐cycle solitons in a Kerr medium. In this paper, we prove the well‐posedness of the classical solutions for the Cauchy problem associated with this equation.

On the solutions for a Benney-Lin type equation

“…In [74], the authors prove that the solution of (8) converges to the solution of (7), while, following [26,19,20,27,66,82], in [23,24], the convergence of the solution of (8) to the unique entropy one of the Burgers equation is proven (see also [22]). Finally, in [36], the well-posedness of the classical solution of the Cauchy problem of ( 8) is proven (see also [18]).…”