## Lie Groups and Their Applications, Volume 1, Issue 1 |

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1-dimensional Abel equation algorithm angular momentum ansatz Applied Mathematics arbitrary function classical coefficients compressive solitary wave Computational condition consider contact transformations coordinate corresponding Coxeter group curvature defined denote dependent derivatives determined differential invariants dimensional Dn+i equivalence transformations Ermakov systems Euler-Lagrange equations evolution equation exact solutions example fundamental solution Fushchich G-invariant Galilean given global generalized solution group transformations Hamiltonian heat equation Huygens independent variables infinitesimal integrals Lagrangian Lie algebra Lie group Lie symmetry Lie-Backlund operator linear partial differential manifolds Math matrix method motion N. H. Ibragimov nonlinear PDEs obtained Olver optimal system ordinary differential equations P G L Leach parameter partial differential equations partial differential operators partially invariant point symmetry point transformation Poisson Bracket problem prolonged pseudospherical surface satisfy scalar second order semilinear sine-Gordon equation solitary wave solitary wave solutions solve space subalgebras submodel symmetry group Theorem theory transformation group two-state