Arrow@dit (Dublin Institute of Technology) · 2010 · 147 citations · 41 references
Natural SciencesMathematicsPhysicsComputational PhysicsDifferential EquationsTheoretical PhysicsInverse ProblemsInverse Problems In MechanicsScattering ProblemsScattering TheorySpectral MethodsSpectral TheoryFundamental SolutionsInverse ScatteringInverse Scattering TransformInverse Spectral ProblemsRiemann - Hilbert ProblemsRiemann-hilbert ProblemsScattering Inverse ProblemsZakharov Equation
We develop the Inverse Scattering Transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method are presented.
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The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
Mark J. Ablowitz, D. J. Kaup, Alan C. Newell et al. · Studies in Applied Mathematics · 1974 · 3.2K citations
Wave breaking for nonlinear nonlocal shallow water equations
Adrian Constantin, Joachim Escher · Acta Mathematica · 1998 · 1.5K citations · Full text