Dynamics of closed-form invariant solutions and diversity of wave profiles of (2+1)-dimensional Ito integro-differential equation via Lie symmetry analysis

New abundant exact solutions for MCBS-nMCBS equation: Painlevé analysis and auto-Bäcklund transformation

“…Here, by opting for particular values for g and u 1 , one can generate exact solutions for (4) by using the first ABT given by (18).…”

“…( 27)-( 29) along with eqs. ( 19) and ( 20) into (18) will generate the analytic solution as u(x, y, t) = η 3 + iη 1 exp (xη 1 + r(t) + yq(t)) 1 + exp (xη 1 + r(t) + yq(t)) , (30) where q(t) is given by eq. ( 28).…”

Abundance of Exact Solutions of a Nonlinear Forced (2 + 1)-Dimensional Zakharov–Kuznetsov Equation for Rossby Waves

“…Also, the exact solutions of these equations are crucial to studying the propagation of Rossby waves [8][9][10][11]. So, many methods have been proposed on how to solve the exact solutions to nonlinear equations, for instance, the Hirota method [12][13][14], the Jacobi elliptic function expansion method [15][16][17][18], the G′/G-expansion method [19][20][21][22][23], the Exp (− Φ(ξ))-expansion method [24,25], the generalised exponential rational function method [26][27][28], the negative power expansion method [29], the hyperbolic function expansion method [30][31][32][33], the extended sub-equation method [34], (ω/g)-expansion method [35], the improved sub-ODE method [36], the Riccati-Bernoulli sub-ODE method [37][38][39][40], the Lie symmetry technique [41][42][43][44][45][46][47], the fractional sub-equation [48] etc. Tese are valid methods and tools for computing nonlinear equations.…”