Soliton perturbation theory for phi-four model and nonlinear Klein–Gordon equations

This paper obtains the adiabatic variation of the soliton velocity, in presence of perturbation terms, of the phi-four model and the nonlinear Klein–Gordon equations. There are three types of models of the nonlinear Klein–Gordon equation, with power law nonlinearity, that are studied in this paper. The soliton perturbation theory is utilized to carry out this investigation.     

Perturbation of topological solitons due to sine-Gordon equation and its type

This paper studies the adiabatic dynamics of topological solitons in presence of perturbation terms. The solitons due to sine-Gordon equation, double sine-Gordon equation, sine–cosine Gordon equation and double sine–cosine Gordon equations are studied, in this paper. The adiabatic variation of soliton velocity is obtained in this paper by soliton perturbation theory.     

Soliton perturbation theory for the generalized fifth-order KdV equation

The soliton perturbation theory is used to study the adiabatic parameter dynamics of solitons due to the generalized fifth-order KdV equation in presence of perturbation terms. The adiabatic change of soliton velocity is also obtained in this paper.     

Optical soliton solutions for the generalized Kudryashov equation of propagation pulse in optical fiber with power nonlinearities by three integration algorithms

In this paper, we employ three integration algorithms, namely, the well‐known Kudryashov method, the new Kudryashov method, and the unified Riccati equation expansion method to extract optical soliton solutions for the generalized Kudryashov equation with power nonlinearities. Straddled soliton, bright solitons, dark solitons, and singular solitons have been found.     

Stochastic perturbation of solitons for Alfven waves in plasmas

The stochastic perturbation of solitons due to Alfven waves in plasmas, is studied in this paper, in addition to the deterministic perturbation terms. The Langevin equations are derived and it is proved that the soliton travels through the plasma with a fixed mean velocity.     

Evolution Theory,Periodic Particles,and Solitons in Cellular Automata

A theory for soliton automata is developed and applied to the analysis and prediction of patterns in their behavior. A complete characterization and method of construction of 1-periodic particles is given. A general evolution theorem (GET) is obtained which provides significant information for a state in terms of preceding states. Application of this theorem yields several interesting results predicting periodicity and solitonic collisions. The GET explains and is based on a fundamental property of soliton automata, observed and analyzed in this paper, namely that pieces of information are lost on the left and reappear on the right.     

Applications of the weighted scheme for GNLS equations in solving soliton solutions

Soliton solutions of a class of generalized nonlinear evolution equations are discussed analytically and numerically, which is achieved using a travelling wave method to formulate one-soliton solution and the finite difference method to the numerical solutions and the interactions between the solitons for the generalized nonlinear Schrödinger equations. The characteristic behavior of the nonlinearity admitted in the system has been investigated and the soliton state of the system in the limit ofα → 0 andα → ∞ has been studied. The results presented show that soliton phenomena are characteristics associated with the nonlinearities of the dynamical systems.     

Soliton perturbation theory for the generalized Benjamin–Bona–Mahoney equation

The soliton perturbation theory is used to study the adiabatic parameter dynamics of solitons due to the Benjamin–Bona–Mahoney equations in presence of perturbation terms. The change in the velocity is also obtained in this paper.     

Relaxation of solitons in nonlinear Schrödinger equations with potential

In this paper we study dynamics of solitons in the generalized nonlinear Schrödinger equation (NLS) with an external potential in all dimensions except for 2. For a certain class of nonlinearities such an equation has solutions which are periodic in time and exponentially decaying in space, centered near different critical points of the potential. We call those solutions which are centered near the minima of the potential and which minimize energy restricted to L²-unit sphere, trapped solitons or just solitons. In this paper we prove, under certain conditions on the potentials and initial conditions, that trapped solitons are asymptotically stable. Moreover, if an initial condition is close to a trapped soliton then the solution looks like a moving soliton relaxing to its equilibrium position. The dynamical law of motion of the soliton (i.e. effective equations of motion for the soliton's center and momentum) is close to Newton's equation but with a dissipative term due to radiation of the energy to infinity.     

Chaos and nonlinear dynamics in financial and nonfinancial time series: Evidence from Finland

This paper contains a set of tests for nonlinearities in economic time series. The tests comprise both standard diagnostic tests for revealing nonlinearities and some new developments in modelling nonlinearities. The latter test procedures make use of models in chaos theory, so-called long-memory models and some asymmetric adjustment models. Empirical tests are carried out with Finnish monthly data for ten macroeconomic time series covering the period 1920–1994. Test results support unambiguously the notion that there are strong nonlinearities in the data. The evidence for chaos, however, is weak. Nonlinearities are detected not only in a univariate setting but also in some preliminary investigations dealing with a multivariate case. Certain differences seem to exist between nominal and real variables in nonlinear behaviour. Some differences are also detected in terms of short and long-term behaviour.     

Existence and multiplicity of solutions for elliptic problems with indefinite discontinuous nonlinearities

In this paper we study the critical points for a locally Lipschitz functional that in some sense will be solutions of an elliptic problem with indefinite discontinuous nonlinearities. We should mention that our results were inspired by the work of Ambrosetti-Badiale [3], Arcoya-Calahorrano [5], Alama-Tarantello [1] and Chang [8]. For the problem studied in [3] we introduce indefinite nonlinearities as in [1] and [6]. To obtain the existence and multiplicity of solutions we use the critical points theory developed by Chang. Applications for Plasma Physics are considered with nonlinearities that change sign. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

APPLICATIONS OF THE P-R SCHEME FOR GENERALIZED NONLINEAR SCHRODINGER EQUATIONS IN SOLVING SOLITON SOLUTIONS

Spatial soliton solutions of a class of generalized nonlinear Schrodinger equations in N-space are discussed analytically and numerically. This achieved using a traveling wavemethod to formulate one-soliton solution and the P-R method is employed to the numerlcal solutions and the interactions between the solirons for the generalized nonlinear systems in Z-pace.The results presented show that the soliton phenomena are characteristics associated with the nonlinearhies of the dynamical systems.     

Painlevé property, auto-Bäcklund transformation and analytic solutions of a variable-coefficient modified Korteweg-de Vries model in a hot magnetized dusty plasma with charge fluctuations

Under investigation in this paper is a variable-coefficient modified Korteweg-de Vries (vc-mKdV) model in a hot magnetized dusty plasma with charge fluctuations. With symbolic computation and bilinear method, Painlevé property is studied, auto-Bäcklund transformation is constructed, while soliton and other analytic solutions are obtained. Furthermore, influence of the coefficients on the dust-ion-acoustic (DIA) solitary wave propagation is investigated based on the soliton solution, which can be concluded as follows: (i) Amplitude of the DIA solitary wave is proportional to the square of the ratio of the coefficients of the dispersive to nonlinear terms; (ii) Velocity of the DIA solitary wave is controlled by the coefficients of the dispersive and dissipative terms; (iii) Propagation trajectory of the DIA solitary wave depends on the function forms of the coefficients of the dispersive, nonlinear and dissipative terms.     

Soliton perturbation theory for the modified nonlinear Schrödinger’s equation

The soliton perturbation theory is used to study the solitons that are governed by the modified nonlinear Schrödinger’s equation. The adiabatic parameter dynamics of the solitons in presence of the perturbation terms are obtained. In particular, the nonlinear gain (damping) and filters or the coefficient of finite conductivity are treated as perturbation terms for the solitons.     

Soliton perturbation theory for nonlinear wave equations

This paper studies the soliton perturbation that are described by three nonlinear wave equations. The adiabatic dynamics of the soliton parameters and the soliton velocity is obtained, in the presence of perturbation terms. The fixed point is also determined in a couple of cases.     

Soliton perturbation theory for the fifth order KdV-type equations with power law nonlinearity

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.     

EXACT SOLUTIONS OF THE VARIABLE COEFFICIENT KdV AND SG TYPE EQUATIONS

In this paper,the variable cofficient KdV equation with dissipative loss and nonuniformity terms and the variable coefficient SG equation with nonuniformity term are studied. The exact solutions of the KdV and SG equations are obtained. In particular,the soliton solutions oftwo equations are found.     

Adiabatic parameter dynamics of perturbed solitary waves

The soliton perturbation theory is used to study the solitons that are governed by the generalized Korteweg–de Vries equation in the presence of perturbation terms. The adiabatic parameter dynamics of the solitons in the presence of the perturbation terms are obtained.     

Asymptotics for Supersonic Soliton Propagation in the Toda Lattice Equation

We study the problem of the adjustment of an initial condition to an exact supersonic soliton solution of the Toda latice equation. Also, we study the problem of soliton propagation in the Toda lattice with slowly varying mass impurities. In both cases we obtain the full numerical solution of the soliton evolution and we develop a modulation theory based on the averaged Lagrangian of the discrete Toda equation. Unlike previous problems with coherent subsonic solutions we need to modify the averaged Lagrangian to obtain the coupling between the supersonic soliton and the subsonic linear radiation. We show how this modified modulation theory explains qualitatively in simple terms the evolution of a supersonic soliton in the presence of impurities. The quantitative agreement between the modulation solution and the numerical result is good.