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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)
##### Keywords:
sinh-Gordon equation
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##### References:
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