Dual Isomonodromic Problems and Whitham Equations

Takasaki, K.: Spectral curves andWhitham equations in isomonodromic problems of Schlesinger type, solv-int/9704004.

Whitham, G. B.: Linear and Nonlinear Waves, WileyInterscience, New York, 1974.

Schlesinger, L.: Über eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten, J. Math. 141 (1912), 96–145.

Itoyama, H. and Morozov, A.: Integrability and Seiberg–Witten theory: Curves and periods, Nuclear Phys. B 477 (1996), 855–877; Prepotential and the Seiberg–Witten theory, hepth/9512161; Marshakov, A.: On integrable systems and supersymmetric gauge theories, hepth/9702083.

Jimbo, M., Miwa, T., Môri, Y. and Sato, M.: Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendents, Physica D 1 (1980), 80–158.

Its, A. R., Izergin, A. G., Korepin, V. E. and Slavnov, N. A.: Differential equations for quantum correlation functions, Internat. J. Modern Phys. B 4 (1990), 1003–1037.

Tracy, C. and Widom, H.: Introduction to random matrices, in Lecture Notes in Phys. 424, SpringerVerlag, Berlin, 1993, pp. 103–130.

Harnad, J.: Dual isomonodromic deformations and moment maps to loop algebras, Comm. Math. Phys. 166 (1994), 337–365.

Adams, M. R., Harnad, J. and Hurtubise, J.: Dual moment maps into loop algebras, Lett. Math. Phys. 20 (1990), 299–308.

Vereschagin, V. L.: Asymptotics of solutions of the discrete string equation, Physica D 95 (1996), 268–282; Nonlinear quasiclassics and Painlevé equations, hepth/9605092.

Adams, M. R., Harnad, J. and Previato, E.: Isospectral Hamiltonian flows in finite and infinite dimensions, I, Comm. Math. Phys. 117 (1988), 451–500. Adams, M. R., Harnad, J. and Hurtubise, J.: ditto II, Comm. Math. Phys. 134 (1990), 555–585.

Beauville, A.: Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta Math. 164 (1990), 211–235.

Flaschka, H. and Newell, A.: Multiphase similarity solutions of integrable evolution equations, Physica D 3 (1981), 203–221.

Krichever, I. M.: The dispersionless Lax equations and topological minimal models, Comm. Math. Phys. 143 (1992), 415–429; The τ-function of the universal Whitham hierarchy, matrix models and topological field theories, Comm. Pure. Appl. Math. 47 (1994), 437–475.

Dubrovin, B. A.: Hamiltonian formalism of Whitham hierarchies and topological LandauGinzburg models, Comm. Math. Phys. 145 (1992), 195–207; Geometry of 2D topological field theories, in Lecture Notes in Math. 1620, SpringerVerlag, Berlin, 1996, pp. 120–348.

Flaschka, H., Forest, M.G. and McLaughlin, D.W.: Multiphase averaging and the inverse spectral solution of the Kortewegde Vries equation, Comm. Pure Appl. Math. 33 (1980), 739–784.

Sklyanin, E. K.: Separation of variables in the Gaudin model, J. Soviet Math. 47 (1989), 2473–2488.

Sklyanin, E. K. and Takebe, T.: Algebraic Bethe ansatz for XYZ Gaudin model, qalg/9601028.

Okamoto, K.: On Fuchs's problem on a torus, I, Funkcial. Ekvac. 14 (1971), 137–152; ditto II, J. Fac. Sci. Univ. Tokyo, Sect. IA 24 (1977), 357–371; Déformation d'une équation differéntielle linéaire avec une singularité irrégulière sur un tore, ibid, 26 (1979), 501–518.