The adiabatic parameter dynamics of solitons, due to fifth order KdV-type equations with power law nonlinearity, is obtained with the aid of soliton perturbation theory. In addition, the small change in the velocity of the soliton, in the presence of perturbation terms, is also determined in this work. c © 2007 Elsevier Ltd. All rights reserved.

This paper studies the Biswas-Milovic equation with log law nonlinearity. TheGausson solution is obtained by the ansatz method. Subsequently, theconservation laws are derived and the conserved quantities are computed usingthe Gausson solution.

This paper obtains the exact 1-soliton solution of the complex GinzburgLandau equation with power law nonlinearity that governs the propagation of solitons through nonlinear optical fibers. The technique that is used to carry out the integration of this equation is He’s semi-inverse variational principle.

The intra-channel collision of optical solitons, with dual-power law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are of Hamil-tonian type. The suppression of soliton-soliton interaction, in presence of these perturbation terms, is acheived. The numerical simulations support the quasi-particle theory.

The Petviashvili’s iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: Mu + u = 0, where M is a positive definite self-adjoint operator and p = const. In this paper, we propose a systematic generalization of this method to both scalar and vector Ha...

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures broad beam evolution at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses and liquid crystals. Novel exact analytical soliton solutions are presented for a generic nonlinearity, within which kn...

We consider arbitrary-angle interactions between spatial solitons and the planar boundary between two optical materials with a single power-law nonlinear refractive index. Extensive analysis has uncovered a wide range of new qualitative phenomena in non-Kerr regimes. A universal Helmholtz-Snell law describing soliton refraction is derived using exact solutions to the governing equation as a non...

The present manuscript begins with a review of the literature on two-tone nonlinearity and proceeds to the description of an ad hoc model of auditory nonlinearity which can account for several of the features of the psychophysical data on various two-tone nonlinearities, in particular, (f2-f1), (2f1-f2), and two-tone suppression. The two basic components of the model are (1) a nonlinearity whic...

Pointing out the difference between the Discrete Nonlinear Schrödinger equation with the classical power law nonlinearity-for which solutions exist globally, independently of the sign and the degree of the nonlinearity, the size of the initial data and the dimension of the lattice-we prove either global existence or nonexistence in time, for the Discrete Klein-Gordon equation with the same type...