Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system

Conservation laws and exact series solution of fractional‐order Hirota–Satsuma‐coupled Korteveg–de Vries system by symmetry analysis

“…Using (16)(17)(18)(19)(20)(21)(22) in (23) and taking all the coefficients of "u" and its derivatives to zero, the set of determining equations for 0 < θ < 1 can be obtained. On solving PDEs and FDEs, the infinitesimal symmetry generators 33 are given below.…”

“…The main framework of evaluating fractional partial differential equations (FPDEs) is to search for exact and approximate solutions of problem, which has been a great task for mathematicians. In order to find exact and approximate solutions of PDEs, researchers projected distinct methods such as the sine–cosine method, tanh method, 8 reduced differential transform method, 9,10 homotopy analysis, 5,11 Lie symmetry analysis, 12–19 and variation iteration method 20 …”

“…[1][2][3][4][5][6][7] The main framework of evaluating fractional partial differential equations (FPDEs) is to search for exact and approximate solutions of problem, which has been a great task for mathematicians. In order to find exact and approximate solutions of PDEs, researchers projected distinct methods such as the sine-cosine method, tanh method, 8 reduced differential transform method, 9,10 homotopy analysis, 5,11 Lie symmetry analysis, [12][13][14][15][16][17][18][19] and variation iteration method. 20 Lie symmetry analysis 21 is powerful tool to generate explicit solution by reducing the given system of FPDEs into a nonlinear system of FODEs with Erdelyi-Kober (EK) fractional differential and integral operators.…”

Conservation Laws and Explicit Solution of system of Fractional-Order Coupled Nonlinear Hirota Equations by Lie Symmetry Analysis

“…New soliton solution of time-fractional Drinfeld-Sokolov-Satsuma-Hirota system in dispersive water waves has been illustrated by Ray et al [48], he claimed the analytical solution with Adomial polynomials and Tanh-method. A generalized two-component Hunter-Saxton system has been studied by Yang et al [49]. Dubey et al [51] has suggested the copulation of fractional homotopy perturbation and fractional homotopy analysis method with Sumudu transforms on local-fractional Laplace equation.…”

Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws

“…A new soliton solution of the time-fractional Drinfeld-Sokolov-Satsuma-Hirota system in dispersive water waves was illustrated by Ray et al [47]. A generalized two-component Hunter-Saxton system was studied by Yang et al [48]. Dubey et al [49] suggested the coupling of the fractional homotopy perturbation and fractional homotopy analysis methods with Sumudu transforms on the local fractional Laplace equation.…”