The integrability conditions and solutions of nonautonomous Hirota equation

• DOI: 10.1007/s11071-017-3787-4
• Publication Date: 2017-09-11T15:30:33Z
• Authors: Limin Pei; Biao Li; Shuwei Xu
• Keywords: 0103 physical sciences; 01 natural sciences

The integrability conditions of nonautonomous Hirota equation are given by using Painleve, Lax pair and similarity transformation methods. When compared with these methods, the Lax pair method allows for the dispersion, nonlinearity, and dissipation coefficients t-dependent, while the Painleve analysis restrict to be t-independent. The integrability conditions of the Painleve analysis method is a special case of our general integrability conditions. Nevertheless, nonautonomous soliton solutions of nonautonomous Hirota equation are obtained from the standard autonomous Hirota equation by similarity transformation, which nontrivially explains their integrability features. The pulse width, shape, height and direction of nonautonomous soliton solutions are variable and depend strongly on both the dispersion and nonlinear profiles. It is clearly demonstrated how to control and optimize the nonautonomous soliton solutions properties by similarity transformation method.