期刊
REGULAR & CHAOTIC DYNAMICS
卷 25, 期 6, 页码 537-543出版社
PLEIADES PUBLISHING INC
DOI: 10.1134/S1560354720060039
关键词
nonlinear mathematical model; traveling wave; solitary wave; pulse propagation; optical fiber
资金
- Russian Foundation for Basic Research [18-29-10025]
A nonlinear fourth-order differential equation with arbitrary refractive index for description of the pulse propagation in an optical fiber is considered. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we look for solutions of the equation using the traveling wave reduction. We present a novel method for finding soliton solutions of nonlinear evolution equations. The essence of this method is based on the hypothesis about the possible type of an auxiliary equation with an already known solution. This new auxiliary equation is used as a basic equation to look for soliton solutions of the original equation. We have found three forms of soliton solutions of the equation at some constraints on parameters of the equation.
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