This manuscript retrieve lump soliton solution for geophysical Korteweg–de Vries equation
(GKdVE) with the help of Hirota bilinear method (HBM). We will also obtain lump–kink …

Symmetry has always played an important role in mechanics, from fundamental formulations
of basic principles to concrete applications. The theme of the book is to develop the basic …

The stability of nonlinear waves has a distinguished history and an abundance of richly
structured yet accessible examples, which makes it not only an important subject but also an …

This survey article is focused on two asymptotic models for internal waves, the Benjamin-
Ono (BO) and Intermediate Long Wave (ILW) equations that are integrable by inverse …

This textbook introduces the well-posedness theory for initial-value problems of nonlinear,
dispersive partial differential equations, with special focus on two key models, the Korteweg …

An overview of various aspects related to the spectral and nonlinear stability of travelling-
wave solutions to partial differential equations is given. The point and the essential spectrum …

We prove in this paper the stability and asymptotic stability in H 1 of a decoupled sum of N
solitons for the subcritical generalized KdV equations The proof of the stability result is …

This book provides a self-contained presentation of classical and new methods for studying
wave phenomena that are related to the existence and stability of solitary and periodic …

We consider the generalized Korteweg-de Vries equations ut+(uxx+ up) x= 0, t, x∈ R, in the
subcritical and critical cases p= 2, 3, 4 or 5. Let Rj (t, x)= Qcj (x− cjt− xj), where j∈{1,..., N}, be …

We consider the generalized Korteweg–de Vries (gKdV) equations in the subcritical cases
p= 2, 3 or 4. The first objective of this paper is to present a direct, simplified proof of the …