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References

  1. W. Bao, D. Jaksch and P.A. Markowich, Numerical solution of the Gross-Pitaevskii Equation for Bose-Einstein condensation, JCP, Vol. 187, No. 1, pp. 318–342, 2003

    MATH  Google Scholar 

  2. L.C. Evans, Partial Differential Equations, AMS, 2002

    Google Scholar 

  3. I. Gasser and P.A. Markowich, Quantum Hydrodynamics, Wigner Transforms and the Classical Limit, Asympt. Analysis, Vol. 14, No. 2, pp. 97–116, 1997

    MATH  Google Scholar 

  4. P. Gerard, P.A. Markowich, N.J. Mauser and F. Poupaud, Homogenization Limits and Wigner Transforms, Comm. Pure and Appl. Math., Vol. 50, pp. 323–378, 1997

    Article  MATH  Google Scholar 

  5. S. Jin and S. Osher, A Level Set Method for the Computation of multivalued Solutions to quasi-linear Hyperbolic PDEs and Hamilton-Jacobi Equations, Comm. Math. Sci. Vol. 1(3), pp. 575–591, 2003

    MATH  Google Scholar 

  6. S. Jin, C.D. Levermore and D.W. McLaughlin, The Semiclassical Limit of the Defocusing Nonlinear Schroedinger Hierarchy, Comm. Pure & Appl. Math. 52, pp. 613–654, 1999

    Article  Google Scholar 

  7. B.B. Kadomtsev and V.I. Petviashili, On the Stability of Solitary Waves in weakly dispersive Media, Sov. Phys. Dokl., 15, pp. 539–541, 1970

    MATH  Google Scholar 

  8. C. Klein, P.A. Markowich and C. Sparber, Numerical Study of Oscillatory Regimes in the Kadomtsev-Petviashili Equation, submitted, 2006

    Google Scholar 

  9. M.D. Kruskal and N.J. Zabusky, Interaction of Solitons in a Collisionless Plasma and the Recurrence of Initial States. Phys. Rev. Lett. 15, pp. 240–243, 1965

    Article  Google Scholar 

  10. P.D. Lax and C.D. Levermore, The Small Dispersion Limit for the Korteweg-deVries Equation I, Comm. Pure & Appl. Math. 36, pp. 253–290, 1983

    Article  MATH  Google Scholar 

  11. P.D. Lax and C.D. Levermore, The Small Dispersion Limit for the Korteweg-deVries Equation II, Comm. Pure & Appl. Math. 36, pp. 571–593, 1983

    Article  MATH  Google Scholar 

  12. P.D. Lax and C.D. Levermore, The Small Dispersion Limit for the Korteweg-deVries Equation III, Comm. Pure & Appl. Math. 36, pp. 809–830, 1983

    Article  MATH  Google Scholar 

  13. P.-L. Lions and T. Paul, Sur les mesures de Wigner. Rev. Mat. Iberoam. 9, pp. 553–618, 1993

    MATH  Google Scholar 

  14. P. A. Markowich, N. Mauser and C. Sparber, Multivalued Geometrical Optics: Wigner Functions versus WKB-Methods, Asymptotic Analysis 33(2), pp. 153–187, 2003

    MATH  Google Scholar 

  15. L.P. Pitaevskii, Zh. Eksp. Teor. Fiz 40, 646, 1961 (Sov. Phys. JETP 13, 451, 1961

    Google Scholar 

  16. J. Smoller, Shock-Waves and Reaction-Diffusion Systems, Springer, 1983

    Google Scholar 

  17. J.H. Stocker, G.J. Komen, L. Cavaleri, Dynamics and Modelling of Ocean Waves, Cambridge University Press, 2006

    Google Scholar 

  18. C. Sulem and P.-L. Sulem, The Nonlinear Schroedinger Equation: Selffocusing and Wave Collapse, Appl. Math. Sciences, Volume 139, Springer, 1999

    Google Scholar 

  19. W. Thirring, Lehrbuch der Mathematischen Physik 4-Quantenmechanik grosser Systeme. Springer Wien-New York, 1980

    MATH  Google Scholar 

  20. E. Wigner, On the Quantum Correction for Thermodynamic Equilibrium, Phys. Rev. 40, pp. 749–759, 1932

    Article  MATH  Google Scholar 

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(2007). Wave Equations. In: Applied Partial Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34646-3_10

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