On singular solutions of the nonlinear Schroedinger and Zakharov equations

Thesis/Dissertation · Mon Jan 01 04:00:00 EST 1990

OSTI ID:5727807

Wang, Xiao Ping

The author studies singular solutions of the nonlinear Schroedinger equation (NLS) with cubic nonlinearity. He also studies the Zakharov equations, which are the model equations for strong Langmuir turbulence. The nonlinear Schroedinger equation is a limit case of the Zakharov equations, the so called subsonic limit. This thesis consists of three parts. In the first part, he considers the NLS and its radically symmetric self-similar singular solutions. In order to study the behavior of singular solutions with general non-symmetric initial data, he introduces an anisotropic dynamic rescaling method which allows him to accurately integrate numerically the NLS up to times very close to the formation of singularities. The numerical results show very clearly that the isotropic singular solutions are stable for a broad class of anisotropic initial perturbations. The second part is devoted to the theoretical study of the above equation for Q. He proves the existence of global, decaying solutions by using the Schauder fixed point theorem. In the third part, he reports results from his recent numerical simulations for the fully three dimensional Zakharov equations, using again the general dynamic rescaling method. He finds both strongly and weakly anisotropic singular solutions. The strongly anisotropic solutions appear to be unstable dynamically.

• Research Organization: New York Univ., NY (United States)
• OSTI ID: 5727807
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ANISOTROPY
DIFFERENTIAL EQUATIONS
EQUATIONS
INTEGRALS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
SINGULARITY
TURBULENCE
WAVE EQUATIONS