Investigation for the exact solutions of two classes of extended Sakovich equations - Li, Zeting; Gao, Ben (Physics letters. A, 2025)
The paper takes two approaches to investigate the exact solutions of two classes of extended Sakovich equations including the extended (3+1)-dimensional variable coefficients Sakovich equation and (2+1)-dimensional fractional Sakovich equation which describe nonlinear wave motion and play an important role in optical fiber and fluid dynamics. We obtain various kinds of solutions for the equations in virtue of two distinct methods. To be more specific, we derive solitary wave, soliton wave and elliptic wave solutions through the use of unified method (UM) and get hyperbolic solution, trigonometric solution and rational solution of them via the modified G′G2-expansion method. Finally, we visualize these solutions by the lights of 3D, 2D and density drawings via selecting appropriate parameters and analyze the propagation characteristics of different kinds of waves and the effect of variable coefficients and derivative order on the soliton wave solutions. Through the analysis for govern models, we can better comprehend the related physical phenomena. •The unified method and modified G′/(G2)-expansion method are used to investigate extend Sakovich equations.•The solitary wave, soliton wave, elliptic wave solution and some standard form solutions of extended Sakovich equations are obtained.•The (2+1)-dimensional Sakovich equation is combined with modified Riemann-Liouville fractional derivative.