We study the dynamical phase diagram of a dilute Bose-Einstein condensate (BEC) trapped
in a periodic potential. The dynamics is governed by a discrete nonlinear Schrödinger …

The mathematical basis of nonlinear optics is Maxwell's system of equations governing
propagation of electromagnetic waves in a material medium, combined with relations …

We study the class of shallow water equations of Camassa and Hold derived from the
Lagrangian, L=∫[1 2 (ϕ xxxx− ϕ x) ϕ t− 1 2 (ϕ x) 3− 1 2 ϕ x (ϕ xx) 2− 1 2 κ ϕ x 2] dx, using a …

Solitons play a fundamental role in the evolution of general initial data for quasilinear
dispersive partial differential equations, such as the Korteweg–de Vries (KdV), nonlinear …

We study two types of bright solitons in zero and non-zero detuning spin–orbit-coupled
(SOC) Bose–Einstein condensates in fractional effect by variational and imaginary-time …

We consider the nonlinear Dirac equations (NLDE's) in 1+ 1 dimension with scalar-scalar
self interaction g 2 k+ 1 (Ψ¯ Ψ) k+ 1, as well as a vector-vector self interaction g 2 k+ 1 (Ψ¯ γ …

In this work, we consider the nonlinear Schrödinger equation (NLSE) in 2+ 1 dimensions
with arbitrary nonlinearity exponent κ in the presence of an external confining potential …

We consider the nonlinear Schrödinger equation (NLSE) in 1+ 1 dimension with scalar-
scalar self-interaction g 2 κ+ 1 (ψ☆ ψ) κ+ 1 in the presence of the external forcing terms of …

Static and dynamic properties of matter-wave solitons in dense Bose–Einstein condensates,
where three-body interactions play a significant role, have been studied by a variational …

This paper considers the P T-symmetric extensions of the equations examined by Cooper,
Shepard and Sodano. From the scaling properties of the P T-symmetric equations a general …