Geodesic
Group analysis of a nonlinear generalization for Black~--- Scholes equation
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 3, pp. 7-14

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Group classification is obtained for an equations family with a free parameter that contains Black — Scholes equation as a partial case. A five-dimensional group of equivalence transformations is calculated and three-dimensional principal Lie algebras in cases of two free element specifications were found. Optimal subalgebras systems and corresponding invariant solutions or invariant submodels are calculated for every Lie algebra.
Keywords: nonlinear partial differential equation, nonlinear Black — Scholes equation, Sircar — Papanicolaou equation, Schönbucher — Wilmott equation, group analysis, invariant solution, invariant submodel. 
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     author = {M. M. Dyshaev},
     title = {Group analysis of a nonlinear generalization for {Black~---} {Scholes} equation},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {7--14},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_3_a1/}
}
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M. M. Dyshaev. Group analysis of a nonlinear generalization for Black~--- Scholes equation. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 3, pp. 7-14. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_3_a1/