New Travelling-Wave Solutions for Dodd-Bullough Equation

A new method, which assumes ϕ' with a function form of f(eϕ), is applied to solve the Dodd-Bullough equation ϕuv=eϕ-e-2ϕ through travelling-wave transformation. A new family of explicit travelling wave solutions is derived. The proposed method works efficiently to be applied to solve other forms of Dodd-Bullough equations

New Travelling Wave Solutions for Sine-Gordon Equation

We propose a method to deal with the general sine-Gordon equation. Several new exact travelling wave solutions with the form of JacobiAmplitude function are derived for the general sine-Gordon equation by using some reasonable transformation. Compared with previous solutions, our solutions are more general than some of the previous

Integrability of the hyperbolic reduced Maxwell-Bloch equations for strongly correlated Bose-Einstein condensates

We derive and study the hyperbolic reduced Maxwell-Bloch equations (HRMB) which acts as a simplified model for the dynamics of strongly correlated Bose-Einstein condensates. A proof of their integrability is found by the derivation of a Lax pair which is valid for both the hyperbolic and standard cases of the reduced Maxwell-Bloch equations. The origin of the latter lies in quantum optics. We derive explicit solutions of the HRMB equations that correspond to kinks propagating on the Bose-Einstein condensate (BEC). These solutions are different from Gross-Pitaevskii solitons because the nonlinearity of the HRMB equations arises from the interaction of the BEC and excited atoms

Exact Travelling Wave Solutions of the Coupled Klein-Gordon Equation by the Infinite Series Method

In this paper, we employ the infinite series method for travelling wave solutions of the coupled Klein-Gordon equations. Based on the idea of the infinite series method, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. The solutions obtained include solitons and periodic solutions

Liouville soliton surfaces obtained using Darboux transformations

We construct parametric Liouville surfaces corresponding to parametric soliton solutions of the Liouville equation and Darboux-transformed counterparts. We also use a modified variation of parameters method together with the elliptic functions method to obtain the traveling wave solutions to Liouville equation and express the centroaffine invariant in terms of the soliton Hamiltonian

The reduced Ostrovsky equation : integrability and breaking

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of Massachusetts Institute of Technology for personal use, not for redistribution. The definitive version was published in Studies in Applied Mathematics 129 (2012): 414–436, doi:10.1111/j.1467-9590.2012.00560.x.The reduced Ostrovsky equation is a modi cation of the Korteweg-de Vries equation, in which the usual linear dispersive term with a third-order deriva- tive is replaced by a linear non-local integral term, which represents the e ect of background rotation. This equation is integrable provided a certain curvature constraint is satis ed. We demonstrate, through theoretical analysis and numeri- cal simulations, that when this curvature constraint is not satisfi ed at the initial time, then wave breaking inevitably occurs.KRH was supported by grant N00014-09-10227 from the Offi ce of Naval Research

Exact Travelling Wave Solutions for Konopelchenko-Dubrovsky Equation by the First Integral Method

In this paper, the first integral method is used to construct exact travelling wave solutions of Konopelchenko-Dubrovsky equation. The first integral method is algebraic direct method for obtaining exact solutions of nonlinear partial differential equations. This method can be applied to non-integrable equations as well as to integrable ones. This method is based on the theory of commutative algebra