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In this paper, the (2 + 1)-dimensional coupled higher-order nonlinear Schrodinger equations are under investigation. The mixed-type vector solitons are derived via Hirota method. The interactions are analyzed graphically mainly on x–t and x–y planes. Moreover, a high intensity pulse, combined solitary waves and bound state solitons are discovered during the interactions. These results are available in optical fiber communication systems.

With the aid of the Painlevé analysis, we obtain residual symmetries for a new (3+1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation. The residual symmetry is localized and the finite transformation is proposed by introducing suitable auxiliary variables. In addition, the interaction solutions of the (3+1)-dimensional gKP equation are constructed via the consistent Riccati expansion method. Particularly, some analytical soliton-cnoidal interaction solutions are discussed in graphical way.

The nonlocal symmetry of the Sawada–Kotera (SK) equation is constructed with the known Lax pair. By introducing suitable and simple auxiliary variables, the nonlocal symmetry is localized and the finite transformation and some new solutions are obtained further. On the other hand, the group invariant solutions of the SK equation are constructed with the classic Lie group method. In particular, by a Galileo transformation some analytical soliton-cnoidal interaction solutions of a asymptotically integrable equation are discussed in graphical ways.

In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higher-order nonlinear Schrödinger equations. In this paper, we will investigate the bright and dark soliton solutions of (2+1)-dimensional coupled higher-order nonlinear Schrödinger equations, with the aid of symbolic computation and the Hirota method. On the basis of soliton solutions, we test and discuss the interactions graphically between the solitons in the x-z, x-t, and z-t planes.