On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations.
Algebro-geometric solutions of the Camassa-Holm hierarchy.
We provide a detailed treatment of the Camassa-Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy is recursively constructed by means of a basic polynomial formalism invoking a spectral parameter. Moreover, we study Dubrovin-type equations for auxiliary divisors and associated trace formulas, consider the corresponding algebro-geometric initial...
Periodic conservative solutions of the Camassa–Holm equation
We show that the periodic Camassa–Holm equation possesses a global continuous semigroup of weak conservative solutions for initial data in . The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure with . The total energy is preserved by the solution.
The short-range expansion in solid state physics
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