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Extended water wave systems of Boussinesq equations on a finite interval: Theory and numerical analysis
Dionyssios Mantzavinos, Dimitrios Mitsotakis
Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe propagation of nonlinear and dispersive water waves of significant interest such as solitary a…
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane
A. Alexandrou Himonas, Dionyssios Mantzavinos
This work studies the initial-boundary value problem of the two-dimensional nonlinear Schrödinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robi…
Growth Bound and Nonlinear Smoothing for the Periodic Derivative Nonlinear Schrödinger Equation
Bradley Isom, Dionyssios Mantzavinos, Atanas Stefanov
A polynomial-in-time growth bound is established for global Sobolev solutions to the derivative nonlinear Schrödinger equation on the circle with . These boun…
The Linearized Classical Boussinesq System on the Half-Line
C. M. Johnston, Clarence T. Gartman, Dionyssios Mantzavinos
The linearization of the classical Boussinesq system is solved explicitly in the case of nonzero boundary conditions on the half-line. The analysis relies on the unified transform…
Polynomial Bound and Nonlinear Smoothing for the Benjamin-Ono Equation on the Circle
Bradley Isom, Dionyssios Mantzavinos, Seungly Oh +1
For initial data in Sobolev spaces , , the solution to the Cauchy problem for the Benjamin-Ono equation on the circle is shown to grow at…
Long-time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions in the Presence of a Discrete Spectrum
Gino Biondini, Sitai Li, Dionyssios Mantzavinos
The long-time asymptotic behavior of solutions to the focusing nonlinear Schrödinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied i…