solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modi ed korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

We consider the soliton solutions in 1and (1+1)-dimensional Toda lattice models with a boundary. We make use of the solutions already known on a full line by means of the Hirota’s method. We explicitly construct the solutions satisfying the boundary conditions. The Z∞-symmetric boundary condition can be introduced by the two-soliton solutions naturally. PACS number: 03.20+i, 02.60Lj

We derive a bound on the energy of the general (p,q)-supersymmetric two-dimensional massive sigma model with torsion, in terms of the topological and Noether charges that appear as central charges in its supersymmetry algebra. The bound is saturated by soliton solutions of first-order Bogomol'nyi-type equations. This generalizes results obtained previously for p = q models without torsion. We g...

The Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions using the ”long wave limit” procedure of Ablowitz and Satsuma, and appropriate ”gauge” transformations. Their properties are also discussed and it is shown that these solutions interact elastically with...

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...

Abstract A multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards the ease of use and capability of computer algebra systems and provides a direct and systematic solution procedure that generalizes Hirota’s perturbation scheme. With the help of Maple, applying the approach to the (3 + 1)-dimensional ...

We consider the generalized Korteweg-de Vries equation ∂tu + ∂ 3 xu + ∂x(u ) = 0, (t, x) ∈ R2, in the supercritical case p > 5, and we are interested in solutions which converge to a soliton in large time in H. In the subcritical case (p < 5), such solutions are forced to be exactly solitons by variational characterization [1, 19], but no such result exists in the supercritical case. In this pa...

The main purpose of this paper is to give a survey of recent development on a classification of soliton solutions of the KP equation. The paper is self-contained, and we give a complete proof for the theorems needed for the classification. The classification is based on the Schubert decomposition of the real Grassmann manifold, Gr(N, M), the set of N -dimensional subspaces in RM . Each soliton ...

Abstract. Binary symmetry constraints are applied to constructing Bäcklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lowerdimensional Liouville integrable systems, which also paves a way for separation of variables and exhibits integrability by quadratures for soliton systems. Illustrative ex...

This paper obtains the solitary wave, shock wave as well as singular soliton solutions to the generalized OstrovskyBenjamin-Bona-Mahoney (gO-BBM) equation. The ansatz method is applied to obtain the solutions. Several constraint conditions for the parameters are derived that establish the existence of the soliton solutions.