We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the dire...

In this paper, the integrable (2+1)-dimensional Maccari system (MS), which can model many complex phenomena in hydrodynamics, plasma physics and nonlinear optics, is investigated by variational approach (VA). This proposed that based on theory Ritz-like method construct explicit solutions via stationary conditions only taking two steps. Finally, dynamic behaviors of are exhibited choosing appro...

‎in this paper we study the existence of nontrivial‎ solutions for a variational inequality on the half-line‎. ‎our‎ ‎approach is based on the non-smooth critical point theory‎ ‎for szulkin-type functionals.

Solitons of a discrete nonlinear Schrödinger equation which includes the next-nearest-neighbor (NNN) interactions are studied by means of a variational approximation (VA) and numerical computations. A large family of multi-humped solutions, including those with a nontrivial intrinsic phase structure, which is a feature particular to the system with the NNN interactions, are accurately predicted...

We develop the technique of the variational approximation for solitons in two directions. First, one may have a physical model which does not admit the usual Lagrangian representation, as some terms can be discarded for various reasons. For instance, the second-harmonic-generation (SHG) model considered here, which includes the Kerr nonlinearity, lacks the usual Lagrangian representation if one...

Abstract Generalized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has gained considerable popularity in recent years, e.g., the analysis multivariate abundance ecology. One main features GLLVMs is their capacity to handle variety responses types, such as (overdispersed) counts, binomial and (semi-)continuous responses, proportions data. O...

the aim of this article is to establish the existence of at least three‎ ‎solutions for a perturbed $p$-biharmonic equation depending on two‎ ‎real parameters‎. ‎the approach is based on variational methods‎.

We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrödinger equations with the attractive self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. ...

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.