The∂ ̄-dressing method is developed to study the three-component coupled Hirota (tcCH)
equations. We first start from a∂ ̄-problem and construct a new spectral problem. Based on …

The aim of this paper is to survey and complete, mostly by numerical simulations, results on
a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. It …

Starting from a 5 * 5 local matrix ̄ ∂-problem, we successfully use the ̄ ∂-dressing
method to derive a hierarchy of nonlinear evolution equations including the nonlinear …

By method of moving frame, the relativistic integrable nonlinear model for real, Majorana
type spinor fields in 1+ 1 dimensions is introduced and gauge equivalence of this model with …

Linear wave theories and stochastic linear wave spectra are foundational to ocean and
coastal engineering. However, there are some important limitations with linear wave …

This dissertation comes in 3 parts. The first consists of a detailed study of the 1+ 1 MKDV
with NZBC. A derivation of MKDV from its Lax Pair is given. Then we construct the …

С использованием метода∂-одевания из локальной (5× 5)-матрицы для∂-задачи
путем введения подходящего оператора рекурсии Λn выведена иерархия нелинейных …

In this note we will discuss a potentially interesting extension of some recent results on
primitive solutions to completely integrable partial differential equations. We will discuss a …