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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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A symmetric parabolic second order PDE

Here I want to solve a second order PDE symmetrically depending on two variables $$ 3(\partial_{\alpha\alpha}f+\partial_{\beta\beta}f-2\partial_{\alpha\beta}f)+2(\cot\alpha)\partial_\alpha f +2(\cot\b …
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