Multi-scale Wave Dynamics in Nonlinear Balance Laws

H. Liu and C. Sparber (2007)

Rigorous Derivation of the Hydrodynamical Equations for Rotating Superfluids, to appear in M3AS.

H. Liu and Z.M. Wang (2007)
Superposition of multi-valued solutions in high frequency wave dynamics,� to appear in Journal of Scientific Computing.
H. Liu and Z.M. Wang,
A field space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations
Journal of Computational Physics, 225 (2007), 591�614.
H. Liu and Z.M. Wang
Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations,
Applied Numerical Mathematics, 57 (2007), 821-836.

H. Liu, S. Osher and R. Tsai,

Multi-valued solution and level set methods in computational high frequency wave propagation, Commun. Comput. Phys. 1(5) (2006), 765-804.
H. Liu
Wave Breaking in a class of nonlocal dispersive wave equations, Journal of Nonlinear Math Phys. 13 (3), (2006), 441-466.
H. Liu and J. Yan
A local discontinuous {G}alerkin method for the {K}orteweg-de {V}ries equation with boundary effect, JCP 215 (2006), 197-218.
H. Liu
Critical Thresholds in the Semiclassical Limit of- 2-D Rotational Schr\"{o}dinger Equations, ZAMP. 57 (2006), 42-58.
H.L. Liu, L.-T. Cheng and S. Osher
A level set framework for capturing  multi-valued solutions to nonlinear first-order equations,  J. Sci. Comp. 29(3) (2006), 353-373. 
S. Jin,
  H.L. Liu, S. Osher and R. Tsai

Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems, JCP, 210(2005), 498-518.

S. Jin,  H.L. Liu, S. Osher and R. Tsai
Computing multivalued physical observables for the semiclassical limit of the Schrodinger equations, 

Journal of Computational Physics, 205(1) (2005), 222-241.

H.L. Liu and M. Slemrod
KdV  Dynamics in the Plasma-Sheath Transition,   Appl. Math. Lett.  17  ( 2004)   401--419.
 L.T. Cheng, H.L. Liu and S. Osher
Computational high frequency wave propagation using the level set method,  with applications to the semi-classical  limit of Schroedinger equations,  Comm. Math. Sci. Vol 1, No. 3 (2003), 593--621.