Introduction: During the summer of 1986, while visiting an old friend in Rio de Janeiro, Brazil, the present author became aware of a significant topological experiment that can be replicated by almost everyone with access to a swimming pool. See Photo 1. In short, it is possible to produce, hydrodynamically, in a surface of discontinuity, a long lived coherent structure that consists of a set ...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

The paper addresses a new “inverse” problem for reconstructing the amplitudes of 2D surface waves from observation of the wave patterns (formed by wave crests). These patterns will depend on the amplitudes because of nonlinear effects. We show that the inverse problem can be solved when the waves are modelled by an equation that supports soliton solutions. Specifically, the explicit solution to...

Over the last two decades, extended objects in field theories called solitons have played an important role in particle physics and astrophysics. In certain cases, these solitons possess a conserved topological charge, which guarantees their stability. There are other extended field configurations, however, which are not topological; these “nontopological solitons” are stable for dynamical reas...

We give a survey of recent development and applications of the chiral quark soliton model (also called the Nambu–Jona-Lasinio soliton model) with Nf=2 and Nf=3 quark flavors for the structure of baryons. The model is an effective chiral quark model obtained from the instanton liquid model of the quantum chromodynamics. Mesons appear as quark-antiquark excitations and baryons arise as non-topolo...

We consider two exit problems for the Korteweg-de Vries equation perturbed by an additive white in time and colored in space noise of amplitude ǫ. The initial datum gives rise to a soliton when ǫ = 0. It has been proved recently that the solution remains in a neighborhood of a randomly modulated soliton for times at least of the order of ǫ. We prove exponential upper and lower bounds for the sm...