A detailed survey of the technique of perturbation theory for nearly integrable systems,
based upon the inverse scattering transform, and a minute account of results obtained by …

Soliton molecules can be formed in some possible mechanisms both theoretically and
experimentally. In this paper, we introduce a new mechanism, namely the velocity resonant …

We derive the nonlinear wave equation for an envelope of an electromagnetic wave in a
monomode dielectric waveguide. Concrete examples are given for a single-mode optical …

It is approximately a quarter of a century since the word" soliton" was first introduced. During
this period, various types of solitons have been discovered in almost all areas of physics …

5. Optical Solitons in Fibers Page 1 5. Optical Solitons in Fibers In this chapter we describe
various properties of optical solitons. 5.1 Soliton Solutions and the Results of Inverse Scattering …

We use asymptotic analysis and a near-identity normal form transformation from water wave
theory to derive a 1+ 1 unidirectional nonlinear wave equation that combines the linear …

Extended shallow water wave equations are derived, using the method of asymptotic
expansions, from the Euler (or water wave) equations. These extended models are valid one …

We investigate the following family of evolutionary 1+ 1 PDEs that describes the balance
between convection and stretching for small viscosity in the dynamics of one-dimensional …

Abstract We derive the Camassa–Holm equation (CH) as a shallow water wave equation
with surface tension in an asymptotic expansion that extends one order beyond the …

In the present study several integrable equations with cubic nonlinearity are derived as
asymptotic models from the classical shallow water theory. The starting point in our …