Soliton Solutions for the Modified KdV6, Modified (2+1)-dimensional Boussinesq, and (3+1)-dimensional KdV Equations - Wazwaz, Abdul-Majid (Journal of Applied Nonlinear Dynamics, 2026)
We study soliton solutions for a modified KdV6 equation, modified Boussinesq equation, and KdV equation in (1+1), (2+1) and (3+1) dimensions respectively. Three distinct new dependent variable trans- formations are combined with the simplified form of Hirota’s direct method is used to achieve these soliton solutions. One soliton solution is formally established for each equation together with its associated dispersion relation and dispersion variable.