Lie symmetries, conservation laws and analytical solutions for two-component integrable equations

Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique

“…Readers are referred to these papers for understanding symmetry, its various variant of definitions, and application of symmetries on PDEs etc. [2][3][4][5][6][7].…”

Diffusion-convection equations and classical symmetry classification

“…Diffusion-convection equations are widely studied in thermal science, however, their symmetries were rarely appeared in open literature. Symmetries of PDE play an important role in thermal science, mechanics, mathematics, and physics, because symmetries can provide important information on the solution properties [1][2][3][4][5], conservation laws [6,7], and variational principle or Hamilton principle [8][9][10][11]. Finding symmetries of an PDE has been caught much attention in various fields.…”

Lie Symmetry Analysis, Optimal Systems and Explicit Solutions of the Dispersive Long Wave Equations

“…generalized simple equation method [21], generalized Tanh function method [22], homotopy perturbation method [23] and power series method [24], etc.) are effectively combined to reflect the complementarity of each other, which makes it possible to obtain exact solutions of some NLPDEs with physical significance, and attracts the attention and research of many scholars [25] [26] [27].…”