Cubic?quartic optical solitons in Lakshmanan?Porsezian?Daniel model derived with semi-inverse variational principle

$(varphi_1, varphi_2)$-variational principle

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

Soliton Solutions of the Perturbed Resonant Nonlinear Schrödinger’s Equation with Full Nonlinearity by Semi-Inverse Variational Principle

This paper carries out the integration of the resonant nonlinear Schrödinger’s equation in presence of perturbation terms that are considered with full nonlinearity. The three types of nonlinear media are studied. They are the cubic nonlinearity, power law and log law nonlinearity. The semi-inverse variational principle is applied to extract the analytical soliton solution.

A Variational Principle for Model-based Morphing

Given a multidimensional data set and a model of its density, we consider how to define the optimal interpolation between two points. This is done by assigning a cost to each path through space, based on two competing goals-one to interpolate through regions of high density, the other to minimize arc length. From this path functional, we derive the Euler-Lagrange equations for extremal motionj ...

A variational principle for model-based interpolation

Given a multidimensional data set and a model of its density, we consider how to deene the optimal interpolation between two points. This is done by assigning a cost to each path through space, based on two competing goals|one to interpolate through regions of high density, the other to minimize arc length. From this path functional, we derive the Euler-Lagrange equations for extremal motion; g...