The algebraic geometric approach to N -component systems of nonlinear integrable PDE’s is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical pheno...

and hosti .2013.08.0 Abstract In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc.) envelope for the underst...

The soliton dressing matrices for the higher-order zeros of the RiemannHilbert problem for theN -wave system are considered. For the elementary higher-order zero, i.e. whose algebraic multiplicity is arbitrary but the geometric multiplicity is 1, the general soliton dressing matrix is derived. The theory is applied to the study of higher-order soliton solutions in the three-wave interaction mod...

‎The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces‎. ‎Quasi-Einstein metrics serve also as solution to the Ricci flow equation‎. ‎Here‎, ‎the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined‎. ‎In compact case‎, ‎it is proved that the quasi-Einstein met...

Abstract: In this paper, we study the application of the known generalized (G ′ G )-expansion method for seeking more exact travelling solutions solutions and soliton solutions of the Kaup-Kupershmidt equation and the (2+1) dimensional breaking soliton equation. As a result, we come to the conclusion that the traveling wave solutions for the two non-linear equations are obtained in three arbitr...

We investigate simulations of exact solutions of the stochastic Dr. Herman Numerical Realizations of Solutions f the Stochastic KdV Equation Exact Solution of Stochastic KdV Wadati 1983 The One Soliton Solution Under Noise Statistical Averages The Exact Solution for < u(x, t) > via the Diffusion Equation Solving the Diffusion Equation The Damped Stochastic KdV Asymptotics Numerical Simulation o...

In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this pa...

In this work we apply the tanh-coth method and the tan-cot method to study some nonlinear coupled equations. Four nonlinear coupled equations that appear in a variety of scientific applications are investigated. We derive soliton, singular solitons and periodic wave solutions for these coupled equations. The obtained results show that these four coupled equations reveal richness of explicit sol...

Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the Hirota bilinear approach. By the Madelung representation, the model transformed to the reaction-diffusion analog of the NLS equation for which the bilinear repres...

Exact stationary soliton solutions of the fifth order KdV type equation ut + αu ux + βu3x + γu5x = 0 are obtained for any p (> 0) in case αβ > 0, Dβ > 0, βγ < 0 (where D is the soliton velocity), and it is shown that these solutions are unstable with respect to small perturbations in case p ≥ 5. Various properties of these solutions are discussed. In particular, it is shown that for any p, thes...