Modified Hirota bilinear method to (3+1)-D variable coefficients generalized shallow water wave equation

The Integrability and Modification to an Auxiliary Function Method for Solving the Strain Wave Equation of a Flexible Rod with a Finite Deformation

“…In the literature, there are several efficient and trustworthy approaches for exploring analytic solutions. Several effective and trustworthy approaches have been introduced in the literature for finding the analytic solutions such as the homogeneous balance method [1,2], Hirota bilinear method [3,4], the Backlund transformation method [5,6], the inverse scattering method [7,8], Semi-inverse variational principle [9,10], algebraic method [11,12], the first integral method [13], an extended mapping technique [14], the Riccati-Bernoulli sub-ODE and exp(G ′ /G)−expansion method [15], the extended exponential function method [16], Lie symmetry analysis [17,18], a modified F-expansion method [19], unified auxiliary equation method [20], three algebraic methods; 1/G ′ , modified G ′ /G 2 and new extended direct algebraic methods [21], the blackuctive perturbation method [22], bifurcation theory [23][24][25][26][27][28], and for other several methods, see, e.g., [29][30][31][32][33][34][35].…”