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On the characteristic Lie algebras for equations \(u_{xy} = f(u, u_x)\). (English. Russian original) Zbl 1158.35312
J. Math. Sci., New York 151, No. 4, 3112-3122 (2008); translation from Fundam. Prikl. Mat. 12, No. 7, 65-78 (2006).
Summary: A new approach to classification of integrable nonlinear equations is proposed. The method is based on description of the structure of the characteristic algebra. A basis of the characteristic algebra is constructed for the sinh-Gordon equation.

MSC:
35A30 Geometric theory, characteristics, transformations in context of PDEs
35L70 Second-order nonlinear hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
58J70 Invariance and symmetry properties for PDEs on manifolds
35Q58 Other completely integrable PDE (MSC2000)
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