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Using advantages of nonstandard computational techniques based on thelight-cone variables, we explicitly find the algebra of generalized symmetriesof the (1+1)-dimensional Klein-Gordon equation. This allows us to describe thisalgebra in terms of the universal enveloping algebra of the essential Lieinvariance algebra of the Klein-Gordon equation. Then we single out variationalsymmetries of the corresponding Lagrangian and compute the space of localconservation laws of this equation, which turns out to be generated, up to theaction of generalized symmetries, by a single first-order conservation law.Moreover, for every conservation law we find a conserved current of minimalorder that is contained in this conservation law.

Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation