On the generation of dispersive shock waves
Copyright policy )On the generation of dispersive shock waves
We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of modulated wavetrains, so-called dispersive shock waves, as the result of shock formation in a limiting dispersionless system. They also provide a detailed description of the solution near caustic curves that delimit dispersive shock waves, revealing fascinating universal wave patterns.
20 pages, 9 figures. Submitted to Physica D
- University of Michigan–Ann Arbor United States
- University of Michigan United States
- Department of Mathematics University of Michigan United States
- University of Michigan–Flint United States
- University of Michigan Ann Arbor United States
semiclassical limit, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Asymptotic behavior of solutions to PDEs, NLS equations (nonlinear Schrödinger equations), FOS: Physical sciences, Pattern Formation and Solitons (nlin.PS), Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Nonlinear Sciences - Pattern Formation and Solitons, Deift-Zhou steepest descent method, Mathematics - Analysis of PDEs, small-dispersion limit, FOS: Mathematics, universality, Exactly Solvable and Integrable Systems (nlin.SI), Lax-Levermore theory, Analysis of PDEs (math.AP)
semiclassical limit, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Asymptotic behavior of solutions to PDEs, NLS equations (nonlinear Schrödinger equations), FOS: Physical sciences, Pattern Formation and Solitons (nlin.PS), Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Nonlinear Sciences - Pattern Formation and Solitons, Deift-Zhou steepest descent method, Mathematics - Analysis of PDEs, small-dispersion limit, FOS: Mathematics, universality, Exactly Solvable and Integrable Systems (nlin.SI), Lax-Levermore theory, Analysis of PDEs (math.AP)
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