Group classification and conservation laws of nonlinear filtration equation with a small parameter

Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations

“…Recently [44] explored deeper these concepts. In [45] approximate conservation laws for a nonlinear filtration equation were established.…”

Conservation laws for time-fractional subdiffusion and diffusion-wave equations

“…Contrary to the solutions ( 28) and ( 29), the solutions (30) and (31) depend on the right time boundary T .…”

“…The correspondence between the symmetries ( 23)-( 25), (27), the constants c i (i = 1, 2, 3, 4) from (31), Table 6: The correspondence between symmetries and conserved vectors numbers for the diffusion-wave equation with the Caputo fractional derivative and the conserved vectors numbers from Table 5 is established by Table 6. Thus, the symmetry X 2 produces all six conservation laws.…”

“…The components of conserved vectors are obtained in this algorithm by acting the so-called Noether operators to a Lagrangian function. Using this approach, the conservation laws for different integer-order differential equations and its systems having only formal Lagrangians have been constructed by their symmetries [23][24][25][28][29][30][31][32][33].…”