Higher-order corrections to the short-pulse equation (Q2851176)

The paper addresses the derivation of higher-order corrections to the short-pulse equation, which was derived from the Maxwell'ss equations for the description of the propagation of short optical pulses, and is integrable, admitting diverse exact solutions, in the form of solitons, soliton-soliton collisions, etc. The form of the integrable equation for real function \(u\) is NEWLINE\[NEWLINE u_{tx} = -(1/2)\chi_0u - (1/2)\chi_3(u^3)_{tt}, NEWLINE\]NEWLINE where \(\chi_0\) and \(\chi_3\) are real coefficients. In this paper, additinal corrections to this equation are derived by means of the renormalization-group method. Effects of the extra terms on single-soliton and two-soliton solutions are investigated by means of numerical simulations.