ABDELOUAHAB KADEM1, DUMITRU BALEANU2,* 1L.M.F.N Mathematics Department, University of Setif, Algeria Email: [email protected] 2Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Çankaya University06530, Ankara, Turkey ∗On leave of absence from Institute of Space Sciences, P.O.BOX, MG-23, RO-077125, Magurele-Bucharest, Romania Emails: [email protected], balea...

In this paper, we are concerned with the integrable decomposition for (2+1)-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. By utilizing recursive relations and symmetric reductions, propose that (n2 − n1 + 1)-flow of AKNS hierarchy can be decomposed into corresponding n1-flow n2-flow (1+1)-dimensional hierarchy, both in coupled reduced cases. As an appropriate generalization, decompos...

In this Letter, we study Kaup-Boussinesq system by using the wellknown He’s variational approach. In fact, the He’s variational method is a promising method to various systems of linear and nonlinear equations.

We construct the traveling wave solutions of the 1 1 -dimensional modified Benjamin-BonaMahony equation, the 2 1 -dimensional typical breaking soliton equation, the 1 1 -dimensional classical Boussinesq equations, and the 2 1 -dimensional Broer-Kaup-Kuperschmidt equations by using an extended G′/G -expansion method, where G satisfies the second-order linear ordinary differential equation. By us...

A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point complete integrability, is presented. Following procedure Ablowitz, Kaup, Newell and Segur (AKNS) we find that version Nonlinear Schrodinger equation, Hirota equation AKNS admit Lax pairs. We report each identified possesses Painleve property for partial differential admits t...

In this paper, we study the possible second order Lax operators for all the possible (1+1)-dimensional models with Schwarz variants and some special types of high dimensional models. It is shown that for every (1+1)-dimensional model and some special types of high dimensional models which possess Schwarz variants may have a second order Lax pair. The explicit Lax pairs for (1+1)-dimensional Kor...

The study of integrable systems is one important topics both in physics and mathematics. However, traditional studies on are usually restricted (1+1) (2+1) dimensions. main reasons come from the fact that high-dimensional extremely rare. Recently, we found a large number high dimensional can be derived low ones by means deformation algorithm. In this paper, Kaup-Newell (KN) system extended to (...

We describe a variational framework for non-commuting flows, extending the theories of Lagrangian multiforms and pluri-Lagrangian systems, which have gained prominence in recent years as description integrable systems sense multidimensional consistency. In context manifold independent variables, often called multi-time, is Lie group whose bracket structure corresponds to commutation relations b...

We consider the modulationally stable version of Kaup–Boussinesq system which models propagation nonlinear waves in various physical situations. It is shown that Whitham modulation equations for this model have a new type solutions describe trigonometric shock waves. In Gurevich–Pitaevskii problem evolution an initial discontinuity, these correspond to nonzero wave excitation on one sides disco...