Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional
equations are well known in anomalous diffusion. We connect these two fields by presenting …

Starting with an integrable nonlinear evolution equation, the author investigates
perturbations about a one-soliton solution, through the inversion of a linear equation for the …

Going back to considerations of Benjamin (1974), there has been significant interest in the
question of stability for the stationary periodic solutions of the Korteweg-deVries equation …

The stability of the stationary periodic solutions of the integrable (one-dimensional, cubic)
defocusing nonlinear Schrödinger (NLS) equation is reasonably well understood, especially …

This work examines the mathematical aspects of nonlinear wave propagation, emphasizing
nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the …

The author applies singular perturbation theory to the study of a damped KdV soliton under
the influence of space-and time-dependent external noise. He finds that asymptotically the …

A numerical wave tank based on the Harmonic Polynomial Cell (HPC) method is created to
study the generation, propagation and interaction of solitary waves. The HPC method has …

The stability of periodic solutions of partial differential equations has been an area of
increasing interest in the last decade. In this paper, we derive all periodic traveling wave …

Under the assumptions of long wavelength, small amplitude and propagation in one
direction, it is well-known that the water wave equations in the lowest order of approximation …

It is well known that the linear stability of solutions of 1+ 1 1+ 1 partial differential equations
which are integrable can be very efficiently investigated by means of spectral methods. We …