The periodic, inverse scattering transform (PIST) is a powerful analytical tool in the theory of integrable, nonlinear evolution equations. Osborne pioneered the use of the PIST in the analysis of data form inherently nonlinear physical processes. In particular, Osborne's so-called nonlinear...

This paper explores the connection between the hydrodynamic mass transport description and the thermodynamic description for a nonlinear range of the Toda lattices. Particular attention is paid to the broken isotropy in the KdV and Burgers equations. The flow variable representation is...

Exact solutions for KdV system equations hierarchy are obtained by using the inverse scattering transform. Exact solutions of isospectral KdV hierarchy, nonisospectral KdV hierarchies and τ-equations related to the KdV spectral problem are obtained by reduction. The interaction of two solitons...

In this paper, a lattice Boltzmann model for the Korteweg–de Vries (KdV) equation with higher-order accuracy of truncation error is presented by using the higher-order moment method. In contrast to the previous lattice Boltzmann model, our method has a wide flexibility to select equilibrium...

A problem in nonlinear water-wave propagation on the surface of an inviscid, stationary fluid is presented.

If the initial condition for the Korteweg–de Vries (KdV) equation is a weakly nonlinear wavepacket, then its evolution is described by the nonlinear Schrödinger (NLS) equation. This KdV/NLS connection has been known for many years, but its various aspects and implications have been discussed...