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This paper is a study of the problem of nonlinear wave motion of the free surface of a body of fluid with a periodically varying bottom. The object is to describe the character of wave propagation inâ€¦ (More)

Many wave phenomena in physics are described by weakly nonlinear nearly monochromatic solutions in the form of modulated wave packets. The examples include ocean waves as well as waves in optics andâ€¦ (More)

A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Daveyâ€“Stewartson II (DSII) equation. Discrete spectrum in the spectral problemâ€¦ (More)

In a fluid system in which two immiscible layers are separated by a sharp free interface, there can be strong coupling between large amplitude nonlinear waves on the interface and waves in theâ€¦ (More)

- Xiao Liu, Gideon Simpson, Catherine Sulem
- J. Nonlinear Science
- 2013

We consider a derivative nonlinear SchrÃ¶dinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability/instabilityâ€¦ (More)

- James Coleman, Catherine Sulem
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2002

We present numerical simulations of blow-up solutions of the vector nonlinear SchrÃ¶dinger equation, which arises as the subsonic limit of the vectorial Zakharov system in plasma physics. In theâ€¦ (More)

- Walid K. Abou Salem, Catherine Sulem
- SIAM J. Math. Analysis
- 2009

The effective dynamics of solitons for the generalized nonlinear SchrÃ¶dinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in spaceâ€¦ (More)

We present a Hamiltonian, potential-flow formulation for nonlinear surface water waves in the presence of a variable bottom. This formulation is based on a reduction of the problem to aâ€¦ (More)

In a recent paper [4], we showed that the phenomenon of resonant tunneling, well known in linear scattering theory, takes place for fast solitons of the Nonlinear SchrÃ¶dinger (NLS) equation in theâ€¦ (More)

- Ehsan Kamalinejad, Robert McCann, +6 authors Dror Bar-Natan
- 2012

An Optimal Transport Approach to Nonlinear Evolution Equations Ehsan Kamalinejad Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2012 Gradient flows of energyâ€¦ (More)