Auto-B�cklund transformations for the nonlinear Schr�dinger equation with variable coefficients

Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation

“…Hence, the discovery of analytical solutions for these equations is crucial in comprehending their dynamics and elucidating the underlying mechanisms governing their existing states. Diverse researchers have successfully employed, developed, and refined a range of innovative approaches to obtain exact solutions for NPDEs, such as the modified and extended rational expansion method [1], the G ′ /(bG ′ + G + a)-expansion technique [2], similarity transformations [3], the Hirota bilinear method [4], the homogenouous balance method [5], the tanh technique [6], Chupin Liu's theorem [7], the first integral technique [8], auto-Backlund transformations [9], the sine-Gordon equation method [10], the modified G ′ /G -expansion method [11], the Riccati equation mapping method [12], the new Kudryashov technique [13], conservation laws [14,15], the Jacobian elliptic function expansion technique [16], Riccati-Bernoulli's sub-ODE technique [17], the sec h p function method [18], Painlevé integrability [19], and so on.…”