One-dimensional optimal system and similarity transformations for the 3+1 Kudryashov-Sinelshchikov equation

We apply the Lie theory to determine the infinitesimal generators of the one-parameter point transformations which leave invariant the 3 + 1 Kudryashov-Sinelshchikov equation. We solve the classification problem of the one-dimensional optimal system, while we derive all the possible independent Lie invariants; that is, we determine all the independent similarity transformations which lead to different reductions. For an application, the results are applied to prove the existence of travel-wave solutions. Furthermore, the method of singularity analysis is applied where we show that the 3 + 1 Kudryashov-Sinelshchikov equation possess the Painleve property and its solution can be written by using a Laurent expansion.

Automated summary

We apply Lie theory to determine the infinitesimal generators of point transformations that leave the 3 + 1 Kudryashov-Sinelshchikov equation invariant. We classify the one-dimensional optimal system and derive all possible independent Lie invariants. The existence of travel-wave solutions is proven using the results, and singularity analysis shows that the equation possesses the Painleve property and solutions can be written using a Laurent expansion.