in this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation.this method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation and c...

Three new iteration methods, namely the squared-operator method, the modified squared-operator method, and the power-conserving squared-operator method, for solitary waves in general scalar and vector nonlinear wave equations are proposed. These methods are based on iterating new differential equations whose linearization operators are squares of those for the original equations, together with ...

The dynamics of a chain of vibrational bonds which develop a classical solitary compression wave is simulated. A converged fully correlated quantum mechanical calculation is compared with a time dependent mean field approach ~TDSCF! and with a classical simulation. The dynamics were all generated from the same Hamiltonian. The TDSCF and classical calculations show a fully developed solitary wav...

A simple nonlinear model is proposed in this paper to study the solitary wave in a circular magneto-electro-elastic rod. Based on the constitutive relation for transversely isotropic piezoelectric and piezomagnetic materials, combined with the differential equations of motion, we derive the longitudinal wave motion equation in a long circular rod. The nonlinearity considered is geometrically as...

We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov–Zhabotinsky reaction confined to thin capillary tubeswhich create a pseudo-one-dimensional system. Theoretical analyses focus on a threevariable reaction–diffusion model that is known to reproduce qualitatively many of the experim...

We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their pr...

The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurance of such a spurious solitary wave, which exhibits a very long life time, results in a nonvanis...

In this paper, based on the known first integral method, we try to seek the traveling wave solutions of several nonlinear evolution equations. As a result, some exact travelig wave solutions and solitary solutions for Whitham-Broer-Kaup (WBK) equations, Gardner equation, Boussinesq-Burgers equations, nonlinear schrodinger equation and mKDV equation are established successfully. Key–Words: First...

where 0&ro&1. The conclusion of the above study is that the solitary waves of the model are dilation stable for 0&co &0.936 and dilation unstable for 0.936 & ro& l. This result agrees with previous numerical results3 and corroborates that the energetic stability criterion is not necessarily correct for spinorial models as some authors claim. In the present work we study the stability under dila...

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...