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In this letter, a (2[Formula: see text]+[Formula: see text]1)-dimensional variable-coefficient Bogoyavlensky-Konopelchenko equation is investigated, which describes the interaction of a Riemann wave propagating along the y-axis and a long wave propagating along the x-axis in a fluid. Under two different constraints of the time-dependent coefficients in this equation, two different bilinear forms are derived by virtue of the binary Bell polynomials. Multiple solitary waves are constructed via the Hirota method, whose propagation properties and interaction characteristics are investigated graphically as well. Propagation and interaction of the solitons are illustrated graphically: (i) time-dependent coefficients affect the shape of the solitons; (ii) interaction of the solitons is elastic, i.e., amplitude, velocity and shape of each soliton remain invariant after each interaction except for a phase shift.

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In this article, under the investigation on the interactions among multiple solitons for an eighth-order nonlinear Schrödinger equation in an optical fibre, oscillations in the interaction zones are observed theoretically. With different coefficients of the operators in this equation, we find that (1) the oscillations in the solitonic interaction zones have different forms with different spectral parameters of this equation; (2) the oscillations in the interactions among the multiple solitons are affected by the choice of spectral parameters, the dispersive effects and nonlinearity of the eighth-order operator; (3) the second-, fifth-, sixth-, and seventh-order operators restrain oscillations in the solitonic interaction zones and the higher-order operators have stronger attenuated effects than the lower ones, while the third- and fourth-order operators stimulate and extend the scope of oscillations.