New (3+1)‐dimensional nonlinear equations with KdV equation constituting its main part: multiple soliton solutions

In thiswork,we present two new(3+1)‐dimensional nonlinear equationswith Korteweg‐de Vries equation constituting its main part. We show that the dispersive relation is distinct for each model, whereas the phase shift remains the same. We determine multiple solitons solutions, with distinct physical structures, for each established equation. The architectures of the simplified Hirota's method is implemented in this paper. The constraint conditions that fall out which must remain valid in order for themultiple solitons to exist are derived.Copyright © 2015 John Wiley & Sons, Ltd.