## Group classification of variable coefficient $$K (m, n)$$ equations.(English)Zbl 1305.35127

Summary: Lie symmetries of $$K(m,n)$$ equations with time-dependent coefficients are classified. Group classification is presented up to widest possible equivalence groups, the usual equivalence group of the whole class for the general case and the conditional equivalence groups for special values of the exponents $$m$$ and $$n$$. Examples on reduction of $$K(m,n)$$ equations (with initial and boundary conditions) to nonlinear ordinary differential equations (with initial conditions) are presented.

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems