The superposition solitons for 3-coupled nonlinear Schrödinger equations

• Hirota bilinear method is developed for applying to the 3-CNLS equations.
• Constructing the exact two-superposition-one-dark one- and two soliton solutions.
• Constructing the exact one-bright-two-superposition one- and two soliton solutions.
• The collision of two solitons is discussed.

In this paper, a Hirota bilinear method is developed for applying to the 3-coupled nonlinear Schrödinger equations. With a reasonable assumption the exact two-superposition-one-dark (TSD) and one-bright-two-superposition (BTS) soliton solutions are constructed analytically. It shows that they can transform into general mixed (dark–bright) soliton solutions in the special conditions. Moreover, the asymptotic behavior analysis shows that the collision of TSD and BTS two solitons are all elastic.