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Research Interest

  • Inverse scattering problem of two or multi-dimensional integrable systems
  • Backlund transformation theory of two or multi-dimensional integrable systems
  • Isomonodromy problem of self similar integrable systems.

Latest Research Work


The Cauchy Problem for the Pavlov equation  (Nonlinearity (2015), v. 28, no. 11, pp. 3709-3754)

P. G. Grinevich, P. M. Santini, and D. Wu

$$v_{xt}+v_{yy}+v_x v_{xy}-v_y v_{xx}=0$$

Abstract: Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data.

Email : mawudc AT
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著作目錄 :

1.  The Cauchy problem for the Pavlov equation with large data, Journal of Differential Equations (2017-03), 1-32(
2.  (with P. G. Grinevich, P. M. Santini) The Cauchy problem for the Pavlov equation, Nonlinearity, arXiv:1310.5834[nlin.SI] , 28(2015), no. 11, 3709-3754
3.  A twisted integrable hierarchy with math symbols by mimetex symmetry, Journal of Mathematical Physics , 53(2012), 103708-103730
4.  (with Hui Ma) Twisted hierarchies associated with the generalized sine-Gordon equation, Journal of Mathematical Physics , 52(2011-04), no. 9, 1-33
5.  The Cauchy problem of the Ward equation, Journal of Functional Analysis , 256(2009-01), no. 1, 215-257
6.  The Cauchy problem of the Ward equation with mixed scattering data, Journal of Mathematical Physics , 49(2008-11), no. 11, 113507-113520
7.  (with Ming-Hsien Tu, Yu-Tung Chen and Jen Hsu Chang) The debar-approach to the dispersionless (2+1)-Harry Dym hierarchy, Journal of Physics A-Mathmatical and General , 38(2005), no. 27, 6167-6181
8.  Isomonodromy deformations for the ZS-AKNS system with quadratic spectral variables, JOURNAL OF MATHEMATICAL PHYSICS , 44(2003), no. 10, 4640-4651
9.  (with D. Pelinovsky) Gauge transformation and spectral decomposition for the Ishimori-II equations, JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL , 36(2003), no. 20, 5557-5574
10.  Global factorization theorems for the ZS-AKNS System, ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS , 77(2002), 1-13
11.  Global Birkhoff factorization on loop groups of the ZS-AKNS flows, Inverse Problems , 18(2002), no. 1, 95-109
12.  (with Y. Lee, A.N. Wang) A bridge for principle harmonic diffeomorphism between surfaces, Ann. Global Analysis and Geometry , 21(2002), no. 2, 141-149
13.  (with Y. Lee and A.N. Wang) A bridge principle for harmonic maps, Ann. Global Analysis and Geometry , 18(2000), no. 2, 107-127
14.  Harmonic diffeomphisms between complete surfaces, Ann. Global Analysis and Geometry , 15(1997), no. 2, 133-139
15.  (with Y. Lee and A.N. Wang) On a theorem of Rado, Bull. London Math. Soc. , 28(1996), no. 4, 398-400
16.  (with Y. Lee) The closed embedded minimal surface in an almost positively curved three manifold, Ann. Global Analysis and Geometry , 13(1995), no. 3, 231-237
17.  A Davey-Stewartson related scattering problem with non small potentials, J. Diff. Equations , 111(1994), no. 1, 27-57
18.  A 2 X 2 scattering problem and its related nonlinear evolutions, Dissertation, Yale University (1990), 0-0