Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution

Non-Lie Reduction Operators and Potential Transformations for a Special System with Applications in Plasma Physics

“…Precise and rigorous definitions for these reductions can be found in [8,14,30]. A number of examples of non-classical reductions for diffusion-type systems are given in the book [31], and in the recent works [32][33][34][35][36]. We can refer to the results derived in this section as potential non-Lie operators for the systems…”

Conservation laws and new exact solutions to the maccari’s modulation equations

“…This application of symmetries (variational symmetry) for finding conservation laws was first established by Noether in his celebrated article [30]. The notion of nonclassical nonlocal symmetry, first introduced by Bluman [31], has become famous to mathematical physicists for its huge applications in finding new classes of exact solutions which can not be obtained by the classical symmetry methods [32]. Among the other methods Tanh method [33], ¢ G G expansion method [34], first integral method [35], sine-cosine method [36], Kudryashov method [37], Jacobi elliptic function method [38], differential constraint method [39], homogeneous balance (HB) method [40,41] etc are widely used in the derivation of exact analytic solutions for nonlinear PDEs.…”