This work recovers cubic-quartic optical solitons with dispersive reflectivity in fiber Bragg
gratings and parabolic law of nonlinearity. The Lie symmetry analysis first reduces the …

In this paper, we employ the inverse scattering approach to study the Poisson structure and
action-angle variables of the complex modified Korteweg-de Vries (cmKdV) equation. We …

In this work, the stability of exact smooth multi-solitons for the Dullin-Gottwald-Holm (DGH)
equation is investigated for the first time. Firstly, through the inverse scattering approach, we …

In this work, the Poisson brackets for the scattering data of an integrable hierarchy for the
Zakharov–Ito system are computed by employ the inverse scattering approach. Then, the …

In this paper, we study a model of generalized Dullin–Gottwald–Holm equation, depending
on the power law nonlinearity, that derives a series of planar dynamical systems. The study …

In this work, we employ the inverse scattering approach to study the Poisson structure and
action-angle variables for the Harry-Dym equation. The Poisson brackets for the scattering …

This paper studies the problem for optimal control of the viscous DGH equation. The
existence and uniqueness of weak solution to the equation are proved in a short interval …

This paper obtains the 1-soliton solution of the generalized Dullin–Gottwald–Holm equation
by the aid of solitary wave ansatz. Subsequently, the conserved quantities are obtained by …

In this work, we employ the inverse scattering transform (IST) to study the action–angle
variables for the Hirota equation. Based on variational principle, we demonstrate that an …

We present an algorithm for the inverse scattering problem associated to the Dullin–
Gottwald–Holm equation, arising in the study of the unidirectional propagation of waves in …