Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation

Self-similar analysis of a viscous heated Oberbeck–Boussinesq flow system

“…There is a considerable analytical and numerical effort to solve Boussinesq approximations or similar forms both for waves [29][30][31][32][33][34][35][36][37][38] and for dissipative dynamics with possible density variations [39][40][41][42][43]. Experiments for certain parameter values are also realized [44][45][46].…”

Closed-form wave structures of the space-time fractional Hirota–Satsuma coupled KdV equation with nonlinear physical phenomena

“…For all the attention, it is an indispensable task to attain the closed-form wave structures of the fractional differential equations (FDEs). Various meaningful and truthful approaches have been interpolated for achieving the closed-form wave structures of FDEs, including the -expansion approach [4,5], extended Jacobi elliptic function expansion method [6], improved sub-equation scheme [7], modified fractional reduced differential transform method [8], sub-equation method [9], singular manifold method [10], fractional homotopy method [11], fractional reduced differential transform method [12], modified ( ′/ ) G G -expansion approach [13], extended modified mapping method [14], Sine-Gordon expansion method [15], extended trial equation method [16], iterative method [17], simplest equation method [18], ansatz scheme [19], F-expansion method [20], modified Kudryashov method [21], extended mapping method [22], homo separation analysis method [23], modified simple equation method [24], reduced differential transform scheme [25], modified extended mapping method [26], functional variable method [27], extended direct algebraic method [28], Darcy's law rule [29], function transformation method [30], the variation of ( ′/ ) G G -expansion method [31], differential transform method [32], unified scheme, ( ′/ ) G G -expansion approach [33,34], Kudryashov method [35], new extended Kudryashov process [36], Sine-cosine approach [37], auxiliary equation scheme [38] and many other techniques…”

Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

“…For deliberative speedy development of symbolic computation systems [1][2][3][4][5], the search for the exact solutions of nonlinear equations has attracted a lot of attention [6][7][8][9] as the exact solutions make it possible to research nonlinear physical phenomena comprehensively and facilitate testing the numerical schemes [10][11][12][13][14]. In the last two decades, various approaches have been proposed and applied to the nonlinear equations of PDEs, such as homogeneous balance method [15,16], extended tanh-function method [17][18][19][20], Jacobi elliptic function expansion method [21], simple equation method [22][23][24], (G/G′)-expansion method [25][26][27], Hirotas bilinear method [28], Exp function method [29], general projective Riccati equation method [30], modified simple equation method [31][32][33], improved direct algebraic technique, [34,35], auxiliary scheme [36] and so on [37][38][39][40][41][42][43]…”