New (3 $$\varvec{+}$$ + 1)-dimensional equations of Burgers type and Sharma–Tasso–Olver type: multiple-soliton solutions

Abstract

We construct new (\(3+1\))-dimensional Burgers and Sharma–Tasso–Olver-type equations. We determine the dispersion relation for each of the newly derived models. By using the simplified Hirota’s method, we derive multiple-soliton solutions for each equation. We derive a generalized dispersion relation that works for both equations.