The zero dispersion limits of nonlinear wave equations

Miscellaneous · Wed Jan 01 00:00:00 EST 1992

OSTI ID:7112684

Tso, T

In chapter 2 the author uses functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schroedinger equation for initial data that satisfy some suitable conditions. In chapter 3 the energy estimates are used to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H[sup 3](R) as [epsilon] [yields] 0; also, it is shown that the strong L[sup 2](R)-limit of the solutions of the BBM equation as [epsilon] [yields] 0 before a critical time. In chapter 4 the author uses the Whitham modulation theory and averaging method to find the 2[pi]-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. It is shown that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, the relations are studied of the KdV equation and the mKdV equation. Finally, the author studies the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.

• Research Organization: Arizona Univ., Tucson, AZ (United States)
• OSTI ID: 7112684
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
WAVE EQUATIONS
BOUNDARY-VALUE PROBLEMS
NONLINEAR PROBLEMS
CONSERVATION LAWS
CONVERGENCE
KLEIN-GORDON EQUATION
KORTEWEG-DE VRIES EQUATION
MODULATION
QUANTUM MECHANICS
SCHROEDINGER EQUATION
DIFFERENTIAL EQUATIONS
EQUATIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
661100* - Classical & Quantum Mechanics- (1992-)