A geometrical approach to the nonlinear solvable equations
A geometrical approach to the nonlinear solvable equations, based on the study of the “groups of motion” of special infinite-dimensional manifolds called “symplectic Kahler manifolds”, is suggested. This approach is constructive, tensorial and simple in its ideas. It allows to recover the equations obtained through the socalled AKNS approach, together with some other examples. It leads to conjecture a possible “integrability condition” for infinite-dimensional systems, and to hope to be able to give a geometrical explanation of the so-called “spectral transform method”.
KeywordsVector Field Configuration Space Homogeneous Boundary Condition Tensor Operator Cotangent Space
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