AN INTEGRABLE SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS ON THE SPECIAL LINEAR GROUP
2002
We give an intrinsic construction of a coupled nonlinear system consisting of two first-order partial differential equations in two dependent and two independent variables which is determined by a hyperbolic structure on the complex special linear group regarded as a real Lie group G. Despite the fact that the system is not Darboux semi-integrable at first order, the construction of a family of solutions depending upon two arbitrary functions, each of one variable, is reduced to a system of ordinary differential equations on the 1-jets. The ordinary differential equations in question are of Lie type and associated with G.
Keywords:
- Stochastic partial differential equation
- Method of characteristics
- Examples of differential equations
- Ordinary differential equation
- Differential algebraic equation
- Mathematical analysis
- Nonlinear system
- Separable partial differential equation
- Mathematics
- Symbol of a differential operator
- Numerical partial differential equations
- Linear differential equation
- Exponential integrator
- Correction
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