A Lie group treatment on a generalized evolution Fisher type equation with variable coefficients

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

“…We used Equation ( 8) to obtain soliton solution under constraints (12) and (13). From balance rules between the higher order and nonlinear term Q ′′ (𝜂) and Q 2n+1 (𝜂), we get N = 1 n .…”

“…However, finding exact solutions to PDEs is generally more challenging than for ordinary differential equations due to the complexity of the equations and the increased number of variables involved. Analytical methods for PDEs include Lie symmetry method [9][10][11], reduction method [12,13], invariant subspace method [14][15][16], and Kudryashov method [17][18][19]. These methods involve advanced mathematical techniques and are essential in understanding various physical and natural phenomena, including fluid dynamics, heat transfer, and electromagnetic fields.…”