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Nonlinear superposition of simple waves on a simple state
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algebraic anihilator arbitrary function assumption Burnat called Cauchy problem characteristic fields characteristic vectors coefficients commutator conditions of involution covector decays Definition denote dependent variables described determine equation 5.9 example exp f fluid following conditions formulae Frobenius theorem func given gradient catastrophy Grundland 1979 Grundland A.M. Hence hodograph space H homogeneous system hyperbolic system hyperplanes initial conditions integral curve integral manifolds interaction of waves invariants g2 involution system Let us assume Let us consider Lie modulus linear linearly independent magnetic field matrix module neighbourhood nonhomogeneous equations nonhomogeneous system obtain oddziaływania one-form parameter parametric form partial differential equations Peradzyriski Pfaff's system physical point Uq process of interaction reduced region of interaction respect Riemann invariants satisfying the equation simple integral elements simple waves simple waves propagating Sine-Gordon equation supp system of equations tangent mapping du(x tangent space tangent vector tion unknown functions vanish vector fields velocity