33 citations · 129 across the 14 of their papers we have counts for
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On the nonlinear dynamics of the traveling-wave solutions of the Serre system
Dimitrios Mitsotakis, Denys Dutykh, John D. Carter
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and t…
Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schrodinger equation
Roger J. Thelwell, John D. Carter, Bernard Deconinck
The two-dimensional cubic nonlinear Schrodinger equation admits a large family of one-dimensional bounded traveling-wave solutions. All such solutions may be written in terms of an…
Instabilities in the two-dimensional cubic nonlinear Schrodinger equation
John D. Carter, Harvey Segur
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers.…