We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the co...

Interacting with a Scalar Wave Field Alexander Komech1 Department of Mechanics and Mathematics of Moscow State University, Moscow 119899, Russia email: [email protected] Herbert Spohn Theoretische Physik, Ludwig-Maximilians-Universit at Theresienstrasse 37, D-80333 M unchen, Germany email: [email protected] AbstractWe consider a scalar wave eld translation invariantly coupl...

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equati...

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...

The reductions of the integrable N-wave type equations solvable by the inverse scattering method with the generalized Zakharov-Shabat systems L and related to some simple Lie algebra g are analyzed. The Zakharov-Shabat dressing method is extended to the case when g is an orthogonal algebra. Several types of one soliton solutions of the corresponding N-wave equations and their reductions are stu...

We have found a new class of exact solutions for multicomponent partially coherent solitons in photorefractive media with a drift mechanism of nonlinear response. Their novel feature is that the composite M-component sech-shaped soliton is located on a constant-background plane wave. The solutions are characterized by two free parameters and these are related to the maximum intensity of the com...

In this paper, using ( ′ G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation. Keywords—Exact solution, The (3+1)-dimensiona...

in this paper, based on sinh-cosh method and sinh-gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.these solutions include jacobi elliptic function solution, soliton solution,trigonometric function solution.

In this paper, two types of traveling wave solutions to the osmosis K(2, 2) equation ut + (u 2)x − (u2)xxx = 0 are investigated. They are characterized by two parameters. The expresssions for the soliton and periodic wave solutions are obtained.

We describe wave propagation and soliton localization in photonic lattices, which are induced in a nonlinear medium by an optical interference pattern, taking into account the inherent lattice deformations at the soliton location. We obtain exact analytical solutions and identify the key factors defining soliton mobility, including the effects of gap merging and lattice imbalance, underlying th...