We find explicit (multisoliton) solutions for nonabelian integrable systems such as periodic Toda field equations, Langmuir equations, and Schrödinger equations for functions with values in any associative algebra. The solution for nonabelian Toda field equations for root systems of types A, B, C was expressed by the authors in [EGR] using quasideterminants introduced and studied in [GR1-GR4]. ...

70 100 100 100 100 h Discrete: p (n) 1 = 6 12 = 0.5 p (n) 1|1 = 3 3 = 1, p (n) 1|2 = 3 3 = 1, p (n) 1|3 = 0 3 = 0, p (n) 1|4 = 0 3 = 0 Continuous: p (n) 1 = 1 12 (σ(100) + σ(70) + . . .+ σ(−70) + σ(−100)) ≈ 0.5 p (n) 1|1 = 1 3 (σ(100) + σ(70) + σ(100)) ≈ 1 p (n) 1|2 = 1 3 (σ(100) + σ(70) + σ(100)) ≈ 1 p (n) 1|3 = 1 3 (σ(−100) + σ(−70) + σ(−100)) ≈ 0 p (n) 1|4 = 1 3 (σ(−100) + σ(−70) + σ(−100)) ...